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Journal articles on the topic 'Nonlinear complementarity constraints'

Author: Grafiati

Published: 18 January 2023

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1

Goodwin, Graham C., and Maria Marta Seron. "Complementarity Constraints for Nonlinear Systems." IFAC Proceedings Volumes 28, no. 14 (June 1995): 691–96. http://dx.doi.org/10.1016/s1474-6670(17)46909-6.

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2

He, Suxiang, Liwei Zhang, and Jie Zhang. "The Rate of Convergence of a NLM Based on F–B NCP for Constrained Optimization Problems Without Strict Complementarity." Asia-Pacific Journal of Operational Research 32, no. 03 (June 2015): 1550012. http://dx.doi.org/10.1142/s0217595915500128.

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It is well-known that the linear rate of convergence can be established for the classical augmented Lagrangian method for constrained optimization problems without strict complementarity. Whether this result is still valid for other nonlinear Lagrangian methods (NLM) is an interesting problem. This paper proposes a nonlinear Lagrangian function based on Fischer–Burmeister (F–B) nonlinear complimentarity problem (NCP) function for constrained optimization problems. The rate of convergence of this NLM is analyzed under the linear independent constraint qualification and the strong second-order sufficient condition without strict complementarity when subproblems are assumed to be solved exactly and inexactly, respectively. Interestingly, it is demonstrated that the Lagrange multipliers associating with inactive inequality constraints at the local minimum point converge to zeros superlinearly. Several illustrative examples are reported to show the behavior of the NLM.

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3

Zhang, Cong, Limin Sun, and Ya Xiao. "A Generalized Projetion Gradient Algorithm for Mathematical Programs with Complementary Constraints." Journal of Physics: Conference Series 2289, no. 1 (June 1, 2022): 012019. http://dx.doi.org/10.1088/1742-6596/2289/1/012019.

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Abstract Against the shortcomings that many existing algorithms for solving the standard smoothing nonlinear programming would fail if they were used directly to solve the mathematical programs with complementary constraints( MPCC). By using a complementarity function and the idea of smoothing approximation method, the MPCC problem was transformed into a smoothing nonlinear programming. Combined with the supermemory gradient idea, a generalized projection gradient algorithm is proposed and its global convergence is obtained.

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4

Fletcher*, Roger, and Sven Leyffer,‡. "Solving mathematical programs with complementarity constraints as nonlinear programs." Optimization Methods and Software 19, no. 1 (February 2004): 15–40. http://dx.doi.org/10.1080/10556780410001654241.

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5

Jiang, Houyuan, and Daniel Ralph. "Smooth SQP Methods for Mathematical Programs with Nonlinear Complementarity Constraints." SIAM Journal on Optimization 10, no. 3 (January 2000): 779–808. http://dx.doi.org/10.1137/s1052623497332329.

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6

Zhu, Zhi-bin, Jin-bao Jian, and Cong Zhang. "An SQP algorithm for mathematical programs with nonlinear complementarity constraints." Applied Mathematics and Mechanics 30, no. 5 (May 2009): 659–68. http://dx.doi.org/10.1007/s10483-009-0512-x.

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7

Ferris, Michael, and Henry X. Liu. "Numerical Studies on Reformulation Techniques for Continuous Network Design with Asymmetric User Equilibria." International Journal of Operations Research and Information Systems 1, no. 1 (January 2010): 52–72. http://dx.doi.org/10.4018/joris.2010101304.

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In this article, we aim to find the most effective reformulation techniques to solve the MPCC (mathematical program with complementarity constraints) model that we proposed recently for continuous network design problems under asymmetric user equilibria. The MPCC model is based on a link-node nonlinear complementarity formulation for asymmetric user equilibria. By applying various reformulation techniques for the lower level nonlinear complementarity, the original bilevel formulation can be converted to a single level nonlinear programming problem. We show that certain reformulations are more effective than others to solve the proposed MPCC model. Recommendations are thus provided on how to choose a reformulation of the continuous network design problem that can be solved effectively and/or efficiently.

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8

Song, Hwachang. "Fuzzy-Enforced Complementarity Constraints in Nonlinear Interior Point Method-Based Optimization." International Journal of Fuzzy Logic and Intelligent Systems 13, no. 3 (September 30, 2013): 171–77. http://dx.doi.org/10.5391/ijfis.2013.13.3.171.

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9

Guerra, A., A. M. Newman, and S. Leyffer. "Concrete Structure Design using Mixed-Integer Nonlinear Programming with Complementarity Constraints." SIAM Journal on Optimization 21, no. 3 (July 2011): 833–63. http://dx.doi.org/10.1137/090778286.

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10

Chen, Xinyuan, and Inhi Kim. "Modelling Rail-Based Park and Ride with Environmental Constraints in a Multimodal Transport Network." Journal of Advanced Transportation 2018 (October 4, 2018): 1–15. http://dx.doi.org/10.1155/2018/2310905.

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Environmental sustainability is a significant aspect in the sustainable development of modern urban cities, especially in the road transport system. As traffic demands increase, public transport requires more promotion to accommodate the increasing travel demands while maintaining the environmental quality. Public transport, however, is less attractive in vast suburb areas mainly due to its longer travel distance and waiting time. Therefore, this paper proposes a rail-based Park-and-Ride (RPR) scheme to promote public transport in the multimodal transport network. To remedy the heterogeneous distribution of vehicle pollutants in the network, regulations in environmental sensitive districts are required and studied in this paper. To quantitatively evaluate and analyse this joint RPR and environmental regulation strategy in multimodal transport systems, this paper develops an environmental constrained combined modal split and traffic assignment (EC-CMSTA) model. The proposed formulation adopts the concept of fix-point to reformulate the nonlinear complementarity conditions associated with the combined modal split and user equilibrium conditions, which is subsequently incorporated into a VI formulated nonlinear complementarity conditions associated with environmental constraints. The proposed VI formulation can handle a general constraint structure, which enhances the modelling adaptability and flexibility. The strictly monotone and Lipschitz continuity properties of this model are rigorously proved, giving rise to efficient algorithms for the model. A customized projection based self-adaptive gradient projection (SAGP) algorithm is then developed. Numerical studies demonstrate that the EC-MSTA model could enhance the behavioural modelling of network users’ travel decisions and assist in quantitatively evaluating the effectiveness of RPR schemes and environmental regulations.

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11

Ralph, Daniel. "Mathematical programs with complementarity constraints in traffic and telecommunications networks." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1872 (March 6, 2008): 1973–87. http://dx.doi.org/10.1098/rsta.2008.0026.

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Given a suitably parametrized family of equilibrium models and a higher level criterion by which to measure an equilibrium state, mathematical programs with equilibrium constraints (MPECs) provide a framework for improving or optimizing the equilibrium state. An example is toll design in traffic networks, which attempts to reduce total travel time by choosing which arcs to toll and what toll levels to impose. Here, a Wardrop equilibrium describes the traffic response to each toll design. Communication networks also have a deep literature on equilibrium flows that suggest some MPECs. We focus on mathematical programs with complementarity constraints (MPCCs), a subclass of MPECs for which the lower level equilibrium system can be formulated as a complementarity problem and therefore, importantly, as a nonlinear program (NLP). Although MPECs and MPCCs are typically non-convex, which is a consequence of the upper level objective clashing with the users' objectives in the lower level equilibrium program, the last decade of research has paved the way for finding local solutions of MPCCs via standard NLP techniques.

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12

Petoussis, S. G., X. P. Zhang, and K. R. Godfrey. "Electricity market equilibrium analysis based on nonlinear interior point algorithm with complementarity constraints." IET Generation, Transmission & Distribution 1, no. 4 (2007): 603. http://dx.doi.org/10.1049/iet-gtd:20050541.

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13

Zhang, Cong, Limin Sun, Zhibin Zhu, and Minglei Fang. "An Implicit Smooth Conjugate Projection Gradient Algorithm for Optimization with Nonlinear Complementarity Constraints." Applied Mathematics 06, no. 10 (2015): 1712–26. http://dx.doi.org/10.4236/am.2015.610152.

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14

Sun, Wei, Sam Harrison, and Gareth P. Harrison. "Value of Local Offshore Renewable Resource Diversity for Network Hosting Capacity." Energies 13, no. 22 (November 12, 2020): 5913. http://dx.doi.org/10.3390/en13225913.

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It is imperative to increase the connectable capacity (i.e., hosting capacity) of distributed generation in order to decarbonise electricity distribution networks. Hybrid generation that exploits complementarity in resource characteristics among different renewable types potentially provides value for minimising technical constraints and increasing the effective use of the network. Tidal, wave and wind energy are prominent offshore renewable energy sources. It is of importance to explore their potential complementarity for increasing network integration. In this work, the novel introduction of these distinct offshore renewable resources into hosting capacity evaluation enables the quantification of the benefits of various resource combinations. A scenario reduction technique is adapted to effectively consider variation of these renewables in an AC optimal power flow-based nonlinear optimisation model. Moreover, the beneficial impact of active network management (ANM) on enhancing the renewable complementarity is also investigated. The combination of complementary hybrid generation and ANM, specifically where the maxima of the generation profiles rarely co-occur with each other and with the demand minimum, is found to make the best use of the network components.

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15

Chen, Yuan-yuan, and Yan Gao. "Levenberg-Marquardt Method for the Eigenvalue Complementarity Problem." Scientific World Journal 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/307823.

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The eigenvalue complementarity problem (EiCP) is a kind of very useful model, which is widely used in the study of many problems in mechanics, engineering, and economics. The EiCP was shown to be equivalent to a special nonlinear complementarity problem or a mathematical programming problem with complementarity constraints. The existing methods for solving the EiCP are all nonsmooth methods, including nonsmooth or semismooth Newton type methods. In this paper, we reformulate the EiCP as a system of continuously differentiable equations and give the Levenberg-Marquardt method to solve them. Under mild assumptions, the method is proved globally convergent. Finally, some numerical results and the extensions of the method are also given. The numerical experiments highlight the efficiency of the method.

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16

Fan, Fujian Duan and Lin. "Superlinear Convergence of a Smooth Approximation Method for Mathematical Programs with Nonlinear Complementarity Constraints." Numerical Mathematics: Theory, Methods and Applications 3, no. 3 (June 2010): 367–86. http://dx.doi.org/10.4208/nmtma.2010.33.6.

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17

Gharbia, Ibtihel Ben, Jad Dabaghi, Vincent Martin, and Martin Vohralík. "A posteriori error estimates for a compositional two-phase flow with nonlinear complementarity constraints." Computational Geosciences 24, no. 3 (January 10, 2020): 1031–55. http://dx.doi.org/10.1007/s10596-019-09909-5.

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18

Jian, Jin-bao. "A Superlinearly Convergent Implicit Smooth SQP Algorithm for Mathematical Programs with Nonlinear Complementarity Constraints." Computational Optimization and Applications 31, no. 3 (July 2005): 335–61. http://dx.doi.org/10.1007/s10589-005-3230-5.

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19

Hu, Qing-Jie, Yun-Hai Xiao, and Y. Chen. "An active set sequential quadratic programming algorithm for nonlinear optimisation." Bulletin of the Australian Mathematical Society 74, no. 1 (August 2006): 69–83. http://dx.doi.org/10.1017/s0004972700035577.

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In this paper, we have proposed an active set feasible sequential quadratic programming algorithm for nonlinear inequality constraints optimization problems. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving a reduced quadratic programming subproblem. To overcome the Maratos effect, a higher-order correction direction is obtained by solving a reduced least square problem. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without strict complementarity.

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20

Wang, Yantao, Xue Lin, and Xian Zhang. "State Feedback Stabilization for Neutral-Type Neural Networks with Time-Varying Discrete and Unbounded Distributed Delays." Journal of Control Science and Engineering 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/517157.

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The problem of stabilization for a class of neutral-type neural networks with discrete and unbounded distributed delays is investigated. By introducing an appropriate Lyapunov-Krasovskii functional and using Jensen inequality technique to deal with its derivative, delay-range-dependent and rate-dependent stabilization criteria are presented in the form of LMIs with nonlinear constraints. In order to solve the nonlinear problem, a cone complementarity linearization (CCL) algorithm is offered. In addition, several numerical examples are provided to illustrate the applicability of the proposed approach.

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21

Adly, Samir, Florent Nacry, and Lionel Thibault. "Discontinuous sweeping process with prox-regular sets." ESAIM: Control, Optimisation and Calculus of Variations 23, no. 4 (May 31, 2017): 1293–329. http://dx.doi.org/10.1051/cocv/2016053.

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In this paper, we study the well−posedness (in the sense of existence and uniqueness of a solution) of a discontinuous sweeping process involving prox-regular sets in Hilbert spaces. The variation of the moving set is controlled by a positive Radon measure and the perturbation is assumed to satisfy a Lipschitz property. The existence of a solution with bounded variation is achieved thanks to the Moreau’s catching-up algorithm adapted to this kind of problem. Various properties and estimates of jumps of the solution are also provided. We give sufficient conditions to ensure the uniform prox-regularity when the moving set is described by inequality constraints. As an application, we consider a nonlinear differential complementarity system which is a combination of an ordinary differential equation with a nonlinear complementarily condition. Such problems appear in many areas such as nonsmooth mechanics, nonregular electrical circuits and control systems.

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22

Dimitriadis, Christos N., Evangelos G. Tsimopoulos, and Michael C. Georgiadis. "A Review on the Complementarity Modelling in Competitive Electricity Markets." Energies 14, no. 21 (November 1, 2021): 7133. http://dx.doi.org/10.3390/en14217133.

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In recent years, the ever-increasing research interest in various aspects of the electricity pool-based markets has generated a plethora of complementarity-based approaches to determine participating agents’ optimal offering/bidding strategies and model players’ interactions. In particular, the integration of multiple and diversified market agents, such as conventional generation companies, renewable energy sources, electricity storage facilities and agents with a mixed generation portfolio has instigated significant competition, as each player attempts to establish their market dominance and realize substantial financial benefits. The employment of complementarity modelling approaches can also prove beneficial for the optimal coordination of the electricity and natural gas market coupling. Linear and nonlinear programming as well as complementarity modelling, mainly in the form of mathematical programs with equilibrium constraints (MPECs), equilibrium programs with equilibrium constraints (EPECs) and conjectural variations models (CV) have been widely employed to provide effective market clearing mechanisms, enhance agents’ decision-making process and allow them to exert market power, under perfect and imperfect competition and various market settlements. This work first introduces the theoretical concepts that regulate the majority of contemporary competitive electricity markets. It then presents a comprehensive review of recent advances related to complementarity-based modelling methodologies and their implementation in current competitive electricity pool-based markets applications.

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23

Anitescu, Mihai. "On Using the Elastic Mode in Nonlinear Programming Approaches to Mathematical Programs with Complementarity Constraints." SIAM Journal on Optimization 15, no. 4 (January 2005): 1203–36. http://dx.doi.org/10.1137/s1052623402401221.

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24

SOON, WANMEI, GONGYUN ZHAO, and JIEPING ZHANG. "Complementarity demand functions and pricing models for multi-product markets." European Journal of Applied Mathematics 20, no. 5 (May 6, 2009): 399–430. http://dx.doi.org/10.1017/s0956792509007918.

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In contrast to single-product pricing models, multi-product pricing models have been much less studied because of the complexity of multi-product demand functions. It is highly non-trivial to construct a multi-product demand function on the entire set of non-negative prices, not to mention approximating the real market demands to a desirable accuracy. Thus, many decision makers use incomplete demand functions which are defined only on a restricted domain, e.g. the set where all components of demand functions are non-negative. In the first part of this paper, we demonstrate the necessity of defining demand functions on the entire set of non-negative prices through some examples. Indeed, these examples show that incomplete demand functions may lead to inferior pricing models. Then we formulate a type of demand functions using a Nonlinear Complementarity Problem (NCP). We call it a Complementarity-Constrained Demand Function (CCDF). We will show that such demand functions possess certain desirable properties, such as monotonicity. In the second part of the paper, we consider an oligopolistic market, where producers/sellers are playing a non-cooperative game to determine the prices of their products. When a CCDF is incorporated into the best response problem of each producer/seller involved, it leads to a complementarity constrained pricing problem facing each producer/seller. Some basic properties of the pricing models are presented. In particular, we show that, under certain conditions, the complementarity constraints in this pricing model can be eliminated, which tremendously simplifies the computation and theoretical analysis.

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25

Oh, Kong Ping. "The Formulation of the Mixed Lubrication Problem as a Generalized Nonlinear Complementarity Problem." Journal of Tribology 108, no. 4 (October 1, 1986): 598–603. http://dx.doi.org/10.1115/1.3261274.

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The mixed-lubrication problem is formulated as a nonlinear generalized complementarity problem in which the pressure acting on the load-bearing surface is taken as the unknown, and the lubricant flow and the gap between the surfaces are taken as its complements. An iterative method was developed to find the solution, which satisfies the complementarity condition that at each point on the load-bearing surface, the pressure or at least one of its complements, is zero at all times. Moreover, the pressure and its complements satisfy non-negativity constraints. The solution intrinsically decomposes the load-bearing surface into three distinct subregions: solid-to-solid contact, hydrodynamically lubricated contact, and no contact (or cavitation). It is shown that the mixed-lubrication formulation degenerates into the special cases of hydrodynamic or solid-to-solid contacts under appropriate load and speed conditions. A journal bearing with elastic support is analyzed to illustrate the method of solution. The transition of the lubrication mode from pure hydrodynamic contact to mixed contact is demonstrated.

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26

Zhang, Meng, Hong Ming Yang, and De Lun Yang. "Simulation and Analysis of Dynamic Evolution of Electricity Market Based on Bidding Decisions with Heterogeneous Expectations." Applied Mechanics and Materials 37-38 (November 2010): 1153–56. http://dx.doi.org/10.4028/www.scientific.net/amm.37-38.1153.

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Based on different bidding decisions with heterogeneous expectations of market participants, a dynamic model of electricity market considering power network constraints is proposed. This model is represented by a discrete difference equations embedded with the optimization problem of market clearing. By using the nonlinear complementarity function, the complex dynamic behaviors of electricity market are simulated and analyzed. The Nash equilibrium and its stability, the periodic and even chaotic dynamic behaviors beyond the stability region of Nash equilibrium are investigated.

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27

Yang, Hongming, C. Y. Chung, Xiaojiao Tong, and Pingping Bing. "Research on dynamic equilibrium of power market with complex network constraints based on nonlinear complementarity function." Journal of Industrial & Management Optimization 4, no. 3 (2008): 617–30. http://dx.doi.org/10.3934/jimo.2008.4.617.

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28

Chen, Qiuxia, Ying Liu, and Haoqi Zhu. "Robust Output Feedback Model Predictive Control for a Class of Networked Control Systems with Nonlinear Perturbation." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/154158.

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This paper is concerned with the design problem of robust dynamic output feedback model predictive controllers for a class of discrete-time systems with time-varying network-induced delays and nonlinear perturbation. The designed controllers achieve on-line suboptimal receding horizon guaranteed cost such that the system can be stabilized for all admissible uncertainties. A novel delay compensation strategy is proposed to eliminate the effects of the time-varying network-induced delays. By using multistep prediction and the receding optimization, the delay-dependent sufficient condition is derived for the existence of delay compensation controllers. By employing the cone complementarity linearization (CCL) idea, a nonlinear minimization problem with linear matrix inequality (LMI) constraints is formulated to design the desired output feedback controllers, and an iterative algorithm involving convex optimization is presented to solve the nonlinear minimization problem. Finally, an example is given to illustrate the feasibility and effectiveness of the proposed results.

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29

XU, HUIFU. "SAMPLE AVERAGE APPROXIMATION METHODS FOR A CLASS OF STOCHASTIC VARIATIONAL INEQUALITY PROBLEMS." Asia-Pacific Journal of Operational Research 27, no. 01 (February 2010): 103–19. http://dx.doi.org/10.1142/s0217595910002569.

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In this paper we apply the well known sample average approximation (SAA) method to solve a class of stochastic variational inequality problems (SVIPs). We investigate the existence and convergence of a solution to the sample average approximated SVIP. Under some moderate conditions, we show that the sample average approximated SVIP has a solution with probability one and with probability approaching one exponentially fast with the increase of sample size, the solution converges to its true counterpart. Finally, we apply the existence and convergence results to SAA method for solving a class of stochastic nonlinear complementarity problems and stochastic programs with stochastic constraints.

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30

Ko, Chun-Hsu, and Jein-Shan Chen. "Optimal Grasping Manipulation for Multifingered Robots Using Semismooth Newton Method." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/681710.

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Multifingered robots play an important role in manipulation applications. They can grasp various shaped objects to perform point-to-point movement. It is important to plan the motion path of the object and appropriately control the grasping forces for multifingered robot manipulation. In this paper, we perform the optimal grasping control to find both optimal motion path of the object and minimum grasping forces in the manipulation. The rigid body dynamics of the object and the grasping forces subjected to the second-order cone (SOC) constraints are considered in optimal control problem. The minimum principle is applied to obtain the system equalities and the SOC complementarity problems. The SOC complementarity problems are further recast as the equations with the Fischer-Burmeister (FB) function. Since the FB function is semismooth, the semismooth Newton method with the generalized Jacobian of FB function is used to solve the nonlinear equations. The 2D and 3D simulations of grasping manipulation are performed to demonstrate the effectiveness of the proposed approach.

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31

Takasu, Keisuke, Yoichi Tanaka, and Masao Fukushima. "Smoothing Method for Nonlinear Second-Order Cone Programs with Complementarity Constraints and Its Application to the Smart House Scheduling Problem." Transactions of the Institute of Systems, Control and Information Engineers 26, no. 1 (2013): 34–44. http://dx.doi.org/10.5687/iscie.26.34.

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32

Dai, Pham Duc. "Optimal Pressure Management in Water Distribution Systems Using an Accurate Pressure Reducing Valve Model Based Complementarity Constraints." Water 13, no. 6 (March 17, 2021): 825. http://dx.doi.org/10.3390/w13060825.

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Water loss according to water leakages in water distribution systems (WDSs) is a challenging problem worldwide. An inappropriate operation of the WDS leads to unnecessarily high pressure distribution in the WDS and thus a large amount of water leakage exists. For this reason, optimal pressure management in WDSs through regulating operations of pressure reducing valves (PRVs) is priority for water utilities. The pressure management can be accomplished in a hierarchical control scheme with high level and low level controllers. While the high level controller is responsible for calculating pressure set points for critical nodes, the task of a low level controller is to regulate the pressures at the critical nodes to the set points. The optimal pressure management in the high level controller can be casted into a nonlinear programing problem (NLP) where PRV models are crucial and determine proper operation of the WDS and quality of overall pressure control. PRV models having been used until now either describe two operating modes (active and open modes) or three operating modes (active, open and check valve modes) with parameter dependence. Such models make the formulated NLP unsuitable for the case PRVs work in check valve modes or resulted in inaccurate NLP solution with unexpected operation modes of PRVs, respectively. Therefore, this paper proposes an accurate PRV model based on complementarity constraints. The new PRV model is parameter-less dependence and is capable of describing complete operation modes of PRVs in practice. As a result, the formulated NLP is general and provides accurate NLP solution. The efficiency of our new PRV model is demonstrated on numerous case studies for optimal pressure management of WDSs.

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33

Zou, Yuan-Yang, and Yu Hu. "An approach of traffic signal control based on NLRSQP algorithm." Modern Physics Letters B 31, no. 31 (November 6, 2017): 1750293. http://dx.doi.org/10.1142/s0217984917502931.

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This paper presents a linear program model with linear complementarity constraints (LPLCC) to solve traffic signal optimization problem. The objective function of the model is to obtain the minimization of total queue length with weight factors at the end of each cycle. Then, a combination algorithm based on the nonlinear least regression and sequence quadratic program (NLRSQP) is proposed, by which the local optimal solution can be obtained. Furthermore, four numerical experiments are proposed to study how to set the initial solution of the algorithm that can get a better local optimal solution more quickly. In particular, the results of numerical experiments show that: The model is effective for different arrival rates and weight factors; and the lower bound of the initial solution is, the better optimal solution can be obtained.

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34

Di, Xuan, Henry X. Liu, Xuegang (Jeff) Ban, and Hai Yang. "Ridesharing User Equilibrium and Its Implications for High-Occupancy Toll Lane Pricing." Transportation Research Record: Journal of the Transportation Research Board 2667, no. 1 (January 2017): 39–50. http://dx.doi.org/10.3141/2667-05.

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Shared mobility—ridesharing in particular—has become an important research topic in recent years because of the ability to relieve traffic congestion, reduce travel costs, and reduce energy consumption. However, researchers in transportation science still lack an understanding of how to incorporate ridesharing into the transportation planning process, specifically in the traffic assignment problem. This paper presents ridesharing user equilibrium (RUE) as a path-flow–based nonlinear complementarity problem with side constraints. This formulation is extended by considering the presence of high-occupancy toll lanes. A numerical example is given to illustrate the relationships of the path cost coefficients on RUE and on the occurrence of the Braess paradox. The performance of two tolling strategies is compared: one charges single-occupancy vehicles, and the other charges both single-occupancy vehicles and vehicles carrying only one passenger.

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35

Yu, Ke, Yanni Yang, and Lang Fan. "Robust Speed Limits Scheme Design for Bimodal Transportation Systems." Mathematical Problems in Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/750694.

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In the context of travel demand uncertainty, this paper investigates how to determine the robust road speed limits for improving mobility and lowering vehicular emissions in bimodal transportation systems that involve private cars and subway. More specifically, the total demand vector is supposed to vary within a given set. Our target is to find the optimal road speed limits against the worst feasible demand scenario so as to minimize the sum social cost of system travel time and vehicular emissions. In order to estimate traffic emissions more reliably, motor vehicle emission simulator (MOVES) is utilized to simulate the emission factor function with respect to average speed. On these bases, we formulate the robust speed limits design problem as a “min-max” nonlinear model with complementarity constraints and solve it iteratively by a cutting-plane scheme that contains two sub-MPCCs. A numerical example is illustrated at the end.

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36

Yano, Hitoshi. "Multiobjective Two-Level Fuzzy Random Programming Problems with Simple Recourses and Estimated Pareto Stackelberg Solutions." Journal of Advanced Computational Intelligence and Intelligent Informatics 22, no. 3 (May 20, 2018): 359–68. http://dx.doi.org/10.20965/jaciii.2018.p0359.

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In this paper, we focus on multiobjective two-level fuzzy random programming problems with simple recourses, in which multiple objective functions are involved in each level, shortages and excesses resulting from the violation of the constraints with fuzzy random variables are penalized, and sums of the objective functions and expectation of the amount of the penalties are minimized. To deal with such problems, the concept of estimated Pareto Stackelberg solutions of the leader is introduced under the assumption that the leader can estimate the preference of the follower as a weighting vector of the weighting problems. Employing the possibility measure for fuzzy numbers, weighting method for multiobjective programming problems, and Kuhn-Tucker approach for two-level programming problems, a nonlinear optimization problem under complementarity conditions is formulated to obtain the estimated Pareto Stackelberg solutions for the leader. A numerical example illustrates the proposed method for a multiobjective two-level fuzzy random programming problem with simple recourses. Several types of estimated Pareto Stackelberg solutions are derived corresponding to the weighting vectors and permissible possibility levels specified by the leader.

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37

Zhang, Lihui, Huiyuan Liu, and Daniel (Jian) Sun. "COMPARISON AND OPTIMIZATION OF CORDON AND AREA PRICINGS FOR MANAGING TRAVEL DEMAND." TRANSPORT 29, no. 3 (May 28, 2014): 248–59. http://dx.doi.org/10.3846/16484142.2014.914970.

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This paper analyses both the cordon and area pricings from the perspective of travel demand management. Sensitivity analysis of various performance measures with respect to the toll rate and demand elastic parameter is performed on a virtual grid network. The analysis shows that cordon pricing mainly affects those trips with origins outside of the Central Business District and destinations inside, while area pricing imposes additional cost on the trips with either origins or destinations in the Central Business District. Though both pricing strategies are able to alleviate traffic congestion in the charging area, area pricing seems more effective, however, area pricing owns the risk to detour too much traffic and thus cause severe congestion to the network outside of the Central Business District. Following the sensitivity analysis, a unified framework is proposed to optimize the designs of the both pricing strategies, which is flexible to account for various practical concerns. The optimization models are formulated as mixed-integer nonlinear programs with complementarity constraints, and the solution procedure is composed of solving a series of nonlinear programs and mixed-integer linear programs. Results from the numerical examples are in line with the findings in the sensitivity analysis. Under the specific network settings, cordon pricing achieves the best system performance when the toll rate reaches the maximum allowed, while area pricing finds the optimal design scheme when the toll rate equals half of the maximum allowed.

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An, Xuena, Shaohua Zhang, Xue Li, and Dajun Du. "Two-stage joint equilibrium model of electricity market with tradable green certificates." Transactions of the Institute of Measurement and Control 41, no. 6 (January 8, 2018): 1615–26. http://dx.doi.org/10.1177/0142331217718619.

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Renewable portfolio standard (RPS) with tradable green certificate (TGC) scheme has important influences on the market equilibrium outcomes and generation firms’ strategic behaviors. The main objective of this paper is to investigate that under the RPS with TGC scheme, who and how to exercise the market power, and to what extent market powers are exercised in the electricity wholesale and TGC markets. This is achieved by firstly proposing a two-stage joint equilibrium model based on the oligopolistic competition equilibrium theory. The model is then formulated as an equilibrium problem with equilibrium constraints (EPEC) by using the backward induction method, which is further solved by the nonlinear complementarity approach. Finally, simulation results show that renewable firms tend to withhold some of TGCs to raise the TGC prices when the RPS is relatively low, otherwise they choose to cut down their electricity output to reduce the volume of TGC and raise the TGC price. Moreover, facing the increasing TGC price, fossil fuel firms tend to withhold their electricity output to decrease the demand of TGCs and lower the TGC price. This study has meaningful implications for design of the electricity markets with TGC market.

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Mangasarian, O. L., and M. V. Solodov. "Nonlinear complementarity as unconstrained and constrained minimization." Mathematical Programming 62, no. 1-3 (February 1993): 277–97. http://dx.doi.org/10.1007/bf01585171.

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Singh, Vikas Vikram, Oualid Jouini, and Abdel Lisser. "Equivalent Nonlinear Complementarity Problem for Chance-constrained Games." Electronic Notes in Discrete Mathematics 55 (November 2016): 151–54. http://dx.doi.org/10.1016/j.endm.2016.10.038.

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Tian, Boshi, Yaohua Hu, and Xiaoqi Yang. "A box-constrained differentiable penalty method for nonlinear complementarity problems." Journal of Global Optimization 62, no. 4 (February 5, 2015): 729–47. http://dx.doi.org/10.1007/s10898-015-0275-6.

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Xu, Liyan, and Bo Yu. "CVaR-constrained stochastic programming reformulation for stochastic nonlinear complementarity problems." Computational Optimization and Applications 58, no. 2 (December 7, 2013): 483–501. http://dx.doi.org/10.1007/s10589-013-9625-9.

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Chen, Yuan-yuan, and Shou-qiang Du. "A New Smoothing Nonlinear Conjugate Gradient Method for Nonsmooth Equations with Finitely Many Maximum Functions." Abstract and Applied Analysis 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/780107.

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The nonlinear conjugate gradient method is of particular importance for solving unconstrained optimization. Finitely many maximum functions is a kind of very useful nonsmooth equations, which is very useful in the study of complementarity problems, constrained nonlinear programming problems, and many problems in engineering and mechanics. Smoothing methods for solving nonsmooth equations, complementarity problems, and stochastic complementarity problems have been studied for decades. In this paper, we present a new smoothing nonlinear conjugate gradient method for nonsmooth equations with finitely many maximum functions. The new method also guarantees that any accumulation point of the iterative points sequence, which is generated by the new method, is a Clarke stationary point of the merit function for nonsmooth equations with finitely many maximum functions.

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Liu, Ailan, and Dingguo Pu. "3-1 Piecewise NCP Function for New Nonmonotone QP-Free Infeasible Method." Journal of Robotics and Mechatronics 26, no. 5 (October 20, 2014): 566–72. http://dx.doi.org/10.20965/jrm.2014.p0566.

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<div class=""abs_img""><img src=""[disp_template_path]/JRM/abst-image/00260005/04.jpg"" width=""300"" />Algorithm flow chart</div> We propose a nonmonotone QP-free infeasible method for inequality-constrained nonlinear optimization problems based on a 3-1 piecewise linear NCP function. This nonmonotone QP-free infeasible method is iterative and is based on nonsmooth reformulation of KKT first-order optimality conditions. It does not use a penalty function or a filter in nonmonotone line searches. This algorithm solves only two systems of linear equations with the same nonsingular coefficient matrix, and is implementable and globally convergent without a linear independence constraint qualification or a strict complementarity condition. Preliminary numerical results are presented. </span>

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Tian, Boshi, Yaohua Hu, and Xiaoqi Yang. "Erratum to: A box-constrained differentiable penalty method for nonlinear complementarity problems." Journal of Global Optimization 62, no. 4 (June 17, 2015): 749. http://dx.doi.org/10.1007/s10898-015-0323-2.

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Li, Chunzhi, Shurong Tong, and Keqin Wang. "Optimal Scheme for Process Quality and Cost Control by Integrating a Continuous Sampling Plan and the Process Yield Index." Discrete Dynamics in Nature and Society 2018 (November 19, 2018): 1–14. http://dx.doi.org/10.1155/2018/1917252.

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The single level continuous sampling plan (CSP-1) is an in-line process control tool that has been commonly adopted in various manufacturing industries. However, CSP-1 is designed for only satisfying the quality constraint. At the same time, CSP-1 has disadvantages with the high probabilities of both Type I and Type II errors due to its inherent deficiency coming from the operating procedure. In this work, an optimal scheme for process quality and cost control is proposed to monitor the process cost and improve the process quality. The CSP-1 and the process yield index (Spk) are integrated in the present scheme, which work independently and complementarily. The four parameters (clearance number, inspecting fraction, sample size, and critical value) are designed in the proposed scheme under simultaneously considering the quality and cost constraints. The sole feasible inspection scheme in CSP-1 under the two constraints is found and used for controlling the process quality. The probabilities of Type I and Type II errors are concurrently controlled at the stipulated level with the risk control scheme, which is constructed with two nonlinear inequation based on the accurate distribution of the index Spk. A case study is illustrated to validate the effectiveness and practicality of the proposed scheme.

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Capasso, Gabriele, Joseph Morlier, Miguel Charlotte, and Simone Coniglio. "Stress-based topology optimization of compliant mechanisms using nonlinear mechanics." Mechanics & Industry 21, no. 3 (2020): 304. http://dx.doi.org/10.1051/meca/2020011.

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The present work demonstrates how a light structure can be easily designed through Topology Optimization even including complex analysis and sizing criteria such as hyperelastic Neo-Hookean materials for nonlinear analysis and aggregated stress constraints. The SIMP approach was adopted and two different strategies were analysed using an in house versatile MATLAB code. MMA was used as reference optimizer (in structural optimization) whereas a unified aggregation and relaxation method was adopted to deal with stress constraints. Feasibility was analyzed from the viewpoint of allowable stress verification. Two test cases are then studied: a morphing airfoil (for aeronautical applications) and a geometric inverter (for mechanics and bio-medical applications). For both, a hyperelastic Neo-Hookean material was chosen. Finally a complementary study on the effects of constraints and the input force intensity is also presented.

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Jian, Jin-Bao, and Chun-Ming Tang. "An SQP feasible descent algorithm for nonlinear inequality constrained optimization without strict complementarity." Computers & Mathematics with Applications 49, no. 2-3 (January 2005): 223–38. http://dx.doi.org/10.1016/j.camwa.2004.09.004.

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Manera, Marc, and David Bacon. "Obtaining nonlinear galaxy bias constraints from galaxy-lensing phase differences." Monthly Notices of the Royal Astronomical Society 506, no. 4 (July 24, 2021): 5878–87. http://dx.doi.org/10.1093/mnras/stab1985.

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ABSTRACT We demonstrate the utility and constraining power of a new statistic for investigating galaxy bias: the galaxy-lensing phase difference. The statistic consists in taking the differences of the phases of the harmonic wave modes between the weak lensing convergence field and the galaxy count field. We use dark matter simulations populated with galaxies up to redshift z = 1 to test the performance of this estimator. We find that phase differences are sensitive to the absolute value of the second-order bias (c2 = b2/b1) and demonstrate why this is the case. For a $1500$ deg2 galaxy survey we recover c2 with an error of approximately 0.1 for a wide range of c2 values; current constraints from redshift surveys have errors of 0.1–0.6 depending on redshift. This new statistic is therefore expected to provide constraints for c2 which are complementary and competitive with constraining power by the conventional estimators from the power spectrum and bispectrum. For the Dark Energy Survey (DES), we predict leading measurements of second-order bias.

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Su, Min, Shu Wei Wang, and Xian Zhang. "Finite-Time Stabilization for Singular Linear Time-Delay Systems with Time-Varying Exogenous Disturbance." Advanced Materials Research 490-495 (March 2012): 2459–63. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.2459.

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In this paper finite-time stabilization for singular linear time-delay systems with time-varying exogenous disturbances is defined. By combining Lyapunov approach and matrix inequality technique, a sufficient condition of the finite-time stabilization for this kind of systems is presented by a set of feasible problems involving linear matrix inequalities (LMIs) with nonlinear constraints. In addition, the nonlinear feasible problems are solved by an so-called cone complementary linearization (CCL) algorithm. The effectiveness of the approach proposed in this paper is presented by a numerical example.

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