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Journal articles on the topic 'Complementarity Constraints'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 June 2024

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1

Júdice, Joaquim. "OPTIMIZATION WITH LINEAR COMPLEMENTARITY CONSTRAINTS." Pesquisa Operacional 34, no. 3 (2014): 559–84. http://dx.doi.org/10.1590/0101-7438.2014.034.03.0559.

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2

Andreani, R., J. J. Júdice, J. M. Martínez, and T. Martini. "Feasibility problems with complementarity constraints." European Journal of Operational Research 249, no. 1 (2016): 41–54. http://dx.doi.org/10.1016/j.ejor.2015.09.030.

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3

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

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4

Klement, Vladimír, Tomáš Oberhuber, and Daniel Ševčovič. "Application of the Level-Set Model with Constraints in Image Segmentation." Numerical Mathematics: Theory, Methods and Applications 9, no. 1 (2016): 147–68. http://dx.doi.org/10.4208/nmtma.2015.m1418.

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AbstractWe propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the segmented objects. Such a-priori information can be expressed in terms of upper and lower constraints prescribed for the level-set function. Constraints have the same conceptual meaning as initial seeds of the popular graph-cuts based methods for image segmentation. A numerical approximation scheme is based on the complementary-finite volumes method c

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5

Deng, Yu, Patrick Mehlitz, and Uwe Prüfert. "Coupled versus decoupled penalization of control complementarity constraints." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 45. http://dx.doi.org/10.1051/cocv/2021022.

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This paper deals with the numerical solution of optimal control problems with control complementarity constraints. For that purpose, we suggest the use of several penalty methods which differ with respect to the handling of the complementarity constraint which is either penalized as a whole with the aid of NCP-functions or decoupled in such a way that non-negativity constraints as well as the equilibrium condition are penalized individually. We first present general global and local convergence results which cover several different penalty schemes before two decoupled methods which are based o

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6

Nguyen, Trang T., Jean-Philippe P. Richard, and Mohit Tawarmalani. "Convexification techniques for linear complementarity constraints." Journal of Global Optimization 80, no. 2 (2021): 249–86. http://dx.doi.org/10.1007/s10898-020-00979-9.

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7

Stein, Oliver. "Lifting mathematical programs with complementarity constraints." Mathematical Programming 131, no. 1-2 (2010): 71–94. http://dx.doi.org/10.1007/s10107-010-0345-y.

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8

Rosehart, W., C. Roman, and A. Schellenberg. "Optimal Power Flow With Complementarity Constraints." IEEE Transactions on Power Systems 20, no. 2 (2005): 813–22. http://dx.doi.org/10.1109/tpwrs.2005.846171.

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9

Outrata, Jiří V. "On mathematical programs with complementarity constraints." Optimization Methods and Software 14, no. 1-2 (2000): 117–37. http://dx.doi.org/10.1080/10556780008805796.

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10

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 (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 s

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11

Kirches, Christian, Jeffrey Larson, Sven Leyffer, and Paul Manns. "Sequential Linearization Method for Bound-Constrained Mathematical Programs with Complementarity Constraints." SIAM Journal on Optimization 32, no. 1 (2022): 75–99. http://dx.doi.org/10.1137/20m1370501.

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12

Chen, Yu, and Zhong Wan. "A New Smoothing Method for Mathematical Programs with Complementarity Constraints Based on Logarithm-Exponential Function." Mathematical Problems in Engineering 2018 (August 12, 2018): 1–11. http://dx.doi.org/10.1155/2018/5056148.

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We present a new smoothing method based on a logarithm-exponential function for mathematical program with complementarity constraints (MPCC). Different from the existing smoothing methods available in the literature, we construct an approximate smooth problem of MPCC by partly smoothing the complementarity constraints. With this new method, it is proved that the Mangasarian-Fromovitz constraint qualification holds for the approximate smooth problem. Convergence of the approximate solution sequence, generated by solving a series of smooth perturbed subproblems, is investigated. Under the weaker

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13

Benita, Francisco, and Patrick Mehlitz. "Optimal Control Problems with Terminal Complementarity Constraints." SIAM Journal on Optimization 28, no. 4 (2018): 3079–104. http://dx.doi.org/10.1137/16m107637x.

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14

Hu, Jing, John E. Mitchell, Jong-Shi Pang, and Bin Yu. "On linear programs with linear complementarity constraints." Journal of Global Optimization 53, no. 1 (2011): 29–51. http://dx.doi.org/10.1007/s10898-010-9644-3.

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15

Wu, Jia, Liwei Zhang, and Yi Zhang. "Mathematical Programs with Semidefinite Cone Complementarity Constraints: Constraint Qualifications and Optimality Conditions." Set-Valued and Variational Analysis 22, no. 1 (2013): 155–87. http://dx.doi.org/10.1007/s11228-013-0242-7.

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16

BOURGEOT, JEAN-MATTHIEU, and BERNARD BROGLIATO. "TRACKING CONTROL OF COMPLEMENTARITY LAGRANGIAN SYSTEMS." International Journal of Bifurcation and Chaos 15, no. 06 (2005): 1839–66. http://dx.doi.org/10.1142/s0218127405013010.

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In this paper we study the tracking control of Lagrangian systems subject to frictionless unilateral constraints. The stability analysis incorporates the hybrid and nonsmooth dynamical feature of the overall system. The difference between tracking control for unconstrained systems and unilaterally constrained ones, is explained in terms of closed-loop desired trajectories and control signals. This work provides details on the conditions of existence of controllers which guarantee stability. It is shown that the design of a suitable transition phase desired trajectory, is a crucial step. Some s

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17

Leyffer, Sven, Gabriel López-Calva, and Jorge Nocedal. "Interior Methods for Mathematical Programs with Complementarity Constraints." SIAM Journal on Optimization 17, no. 1 (2006): 52–77. http://dx.doi.org/10.1137/040621065.

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18

Júdice, Joaquim J. "Algorithms for linear programming with linear complementarity constraints." TOP 20, no. 1 (2011): 4–25. http://dx.doi.org/10.1007/s11750-011-0228-2.

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19

Ye, J. J. "Optimality Conditions for Optimization Problems with Complementarity Constraints." SIAM Journal on Optimization 9, no. 2 (1999): 374–87. http://dx.doi.org/10.1137/s1052623497321882.

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20

Wachsmuth, Gerd. "Mathematical Programs with Complementarity Constraints in Banach Spaces." Journal of Optimization Theory and Applications 166, no. 2 (2014): 480–507. http://dx.doi.org/10.1007/s10957-014-0695-3.

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21

Bai, Lijie, John E. Mitchell, and Jong-Shi Pang. "On convex quadratic programs with linear complementarity constraints." Computational Optimization and Applications 54, no. 3 (2012): 517–54. http://dx.doi.org/10.1007/s10589-012-9497-4.

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22

Xu, Liyan, Bo Yu, and Wei Liu. "The Distributionally Robust Optimization Reformulation for Stochastic Complementarity Problems." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/469587.

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We investigate the stochastic linear complementarity problem affinely affected by the uncertain parameters. Assuming that we have only limited information about the uncertain parameters, such as the first two moments or the first two moments as well as the support of the distribution, we formulate the stochastic linear complementarity problem as a distributionally robust optimization reformation which minimizes the worst case of an expected complementarity measure with nonnegativity constraints and a distributionally robust joint chance constraint representing that the probability of the linea

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23

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 (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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24

Wang, Guangmin, Junwei Yu, and Shubin Li. "An MPCC Formulation and Its Smooth Solution Algorithm for Continuous Network Design Problem." PROMET - Traffic&Transportation 29, no. 6 (2017): 569–80. http://dx.doi.org/10.7307/ptt.v29i6.2250.

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Continuous network design problem (CNDP) is searching for a transportation network configuration to minimize the sum of the total system travel time and the investment cost of link capacity expansions by considering that the travellers follow a traditional Wardrop user equilibrium (UE) to choose their routes. In this paper, the CNDP model can be formulated as mathematical programs with complementarity constraints (MPCC) by describing UE as a non-linear complementarity problem (NCP). To address the difficulty resulting from complementarity constraints in MPCC, they are substituted by the Fische

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25

LIU, YONGCHAO, and GUI-HUA LIN. "CONVERGENCE ANALYSIS OF A REGULARIZED SAMPLE AVERAGE APPROXIMATION METHOD FOR STOCHASTIC MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS." Asia-Pacific Journal of Operational Research 28, no. 06 (2011): 755–71. http://dx.doi.org/10.1142/s0217595911003338.

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Regularization method proposed by Scholtes (2011) has been a recognized approach for deterministic mathematical programs with complementarity constraints (MPCC). Meng and Xu (2006) applied the approach coupled with Monte Carlo techniques to solve a class of one stage stochastic MPCC and presented some promising numerical results. However, Meng and Xu have not presented any convergence analysis of the regularized sample approximation method. In this paper, we fill out this gap. Specifically, we consider a general class of one stage stochastic mathematical programs with complementarity constrain

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26

Lidström, P. "Kinematics for unilateral constraints in multibody dynamics." Mathematics and Mechanics of Solids 22, no. 8 (2016): 1654–87. http://dx.doi.org/10.1177/1081286516642270.

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This paper is concerned with the kinematics of unilateral constraints in multibody dynamics. These constraints are related to the contact between parts and the principle of impenetrability of matter and have the property that they may be active, in which case they give rise to constraint forces, or passive, in which case they do not give rise to constraint forces. In order to check whether the constraint is active or passive a distance function between parts of the multibody is required. The paper gives a rigorous definition of the distance function and derives certain of its properties. The u

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27

Lin, Gui-Hua, and Masao Fukushima. "Regularization method for stochastic mathematical programs with complementarity constraints." ESAIM: Control, Optimisation and Calculus of Variations 11, no. 2 (2005): 252–65. http://dx.doi.org/10.1051/cocv:2005005.

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28

Mangasarian, O. L., and J. S. Pang. "Exact penalty for mathematical programs with linear complementarity constraints." Optimization 42, no. 1 (1997): 1–8. http://dx.doi.org/10.1080/02331939708844347.

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29

Scheel, Holger, and Stefan Scholtes. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity." Mathematics of Operations Research 25, no. 1 (2000): 1–22. http://dx.doi.org/10.1287/moor.25.1.1.15213.

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30

Lin, G. H., and M. Fukushima. "New Relaxation Method for Mathematical Programs with Complementarity Constraints." Journal of Optimization Theory and Applications 118, no. 1 (2003): 81–116. http://dx.doi.org/10.1023/a:1024739508603.

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31

Buong, Nguyen, and Nguyen Thi Thuy Hoa. "Tikhonov regularization for mathematical programs with generalized complementarity constraints." Computational Mathematics and Mathematical Physics 55, no. 4 (2015): 564–71. http://dx.doi.org/10.1134/s0965542515040090.

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32

Birbil, Ş. İlker, Gül Gürkan, and Ovidiu Listeş. "Solving Stochastic Mathematical Programs with Complementarity Constraints Using Simulation." Mathematics of Operations Research 31, no. 4 (2006): 739–60. http://dx.doi.org/10.1287/moor.1060.0215.

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33

Buong, Nguyen, and Nguyen Thi Thuy Hoa. "Tikhonov regularization for mathematical programs with generalized complementarity constraints." Журнал вычислительной математики и математической физики 55, no. 4 (2015): 574. http://dx.doi.org/10.7868/s0044466915040092.

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34

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

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35

Caspari, Adrian, Lukas Lüken, Pascal Schäfer, et al. "Dynamic optimization with complementarity constraints: Smoothing for direct shooting." Computers & Chemical Engineering 139 (August 2020): 106891. http://dx.doi.org/10.1016/j.compchemeng.2020.106891.

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36

Chen, Xiaojun, and Jane J. Ye. "A Class of Quadratic Programs with Linear Complementarity Constraints." Set-Valued and Variational Analysis 17, no. 2 (2009): 113–33. http://dx.doi.org/10.1007/s11228-009-0112-5.

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37

Zhou, Jing, Shu-Cherng Fang, and Wenxun Xing. "Conic approximation to quadratic optimization with linear complementarity constraints." Computational Optimization and Applications 66, no. 1 (2016): 97–122. http://dx.doi.org/10.1007/s10589-016-9855-8.

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38

Lin, Gui-Hua. "Modified relaxation method for mathematical programs with complementarity constraints." Mathematical Methods in the Applied Sciences 30, no. 17 (2007): 2179–95. http://dx.doi.org/10.1002/mma.881.

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39

Thinh, Vo Duc. "On the calm b-differentiability of projector onto circular cone and its applications." Science and Technology Development Journal 23, no. 4 (2020): 727–36. http://dx.doi.org/10.32508/stdj.v23i4.2426.

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In this paper, we study a concept on the calm B-differentiability, a new kind of generalized differentiabilities for a given vector function introduced by Ye and Zhou in 2017, of the projector onto the circular cone. Then, we discuss its applications in mathematical programming problems with circular cone complementarity constraints. Here, this problem can be considered to be a generalization of mathematical programming problems with second-order cone complementarity constraints, and thus it includes a large class of mathematical models in optimization theory. Consequently, the obtained result

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40

Kanno, Yoshihiro. "AN IMPLICIT FORMULATION OF MATHEMATICAL PROGRAM WITH COMPLEMENTARITY CONSTRAINTS FOR APPLICATION TO ROBUST STRUCTURAL OPTIMIZATION." Journal of the Operations Research Society of Japan 54, no. 2-3 (2011): 65–85. http://dx.doi.org/10.15807/jorsj.54.65.

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41

CHEN, YU, and ZHONG WAN. "A LOCALLY SMOOTHING METHOD FOR MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS." ANZIAM Journal 56, no. 3 (2015): 299–315. http://dx.doi.org/10.1017/s1446181115000048.

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We propose a locally smoothing method for some mathematical programs with complementarity constraints, which only incurs a local perturbation on these constraints. For the approximate problem obtained from the smoothing method, we show that the Mangasarian–Fromovitz constraints qualification holds under certain conditions. We also analyse the convergence behaviour of the smoothing method, and present some sufficient conditions such that an accumulation point of a sequence of stationary points for the approximate problems is a C-stationary point, an M-stationary point or a strongly stationary p

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42

Pfeiffer, F. "Complementarity Problems of Stick-Slip Vibrations." Journal of Vibration and Acoustics 118, no. 2 (1996): 177–83. http://dx.doi.org/10.1115/1.2889646.

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Multibody systems with many friction contacts not being decoupled by some force laws afford a special treatment with respect to the uniqueness of the solution after a contact event. This problem can be solved by an optimization technique including unequality constraints which corresponds exactly to the physical properties of stick-slip vibrations. The theoretical background to this complementarity problem is presented and illustrated by examples from machine dynamics.

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43

Sun, Juhe, Xiao-Ren Wu, B. Saheya, Jein-Shan Chen, and Chun-Hsu Ko. "Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete-Type Classes of SOC Complementarity Functions." Mathematical Problems in Engineering 2019 (February 14, 2019): 1–18. http://dx.doi.org/10.1155/2019/4545064.

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This paper focuses on solving the quadratic programming problems with second-order cone constraints (SOCQP) and the second-order cone constrained variational inequality (SOCCVI) by using the neural network. More specifically, a neural network model based on two discrete-type families of SOC complementarity functions associated with second-order cone is proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of SOCQP and SOCCVI. The two discrete-type SOC complementarity functions are newly explored. The neural network uses the two discrete-type families of SOC complementarity functions to

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44

Chen, Yu, and Zhong Wan. "A locally smoothing method for mathematical programs with complementarity constraints." ANZIAM Journal 55 (April 12, 2015): 299. http://dx.doi.org/10.21914/anziamj.v56i0.8170.

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45

Bouza, Gemayqze, Jürgen Guddat, and Georg Still. "Critical sets in one-parametric mathematical programs with complementarity constraints." Optimization 57, no. 2 (2008): 319–36. http://dx.doi.org/10.1080/02331930701779955.

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46

Yan, Tao, and Masao Fukushima. "Smoothing method for mathematical programs with symmetric cone complementarity constraints." Optimization 60, no. 1-2 (2011): 113–28. http://dx.doi.org/10.1080/02331934.2010.541458.

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47

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 (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 o

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48

Kadrani, Abdeslam, Jean-Pierre Dussault, and Abdelhamid Benchakroun. "A New Regularization Scheme for Mathematical Programs with Complementarity Constraints." SIAM Journal on Optimization 20, no. 1 (2009): 78–103. http://dx.doi.org/10.1137/070705490.

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49

Anitescu, Mihai. "Comments on: Algorithms for linear programming with linear complementarity constraints." TOP 20, no. 1 (2011): 26–27. http://dx.doi.org/10.1007/s11750-011-0229-1.

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50

Martínez, J. M. "Comments on: Algorithms for linear programming with linear complementarity constraints." TOP 20, no. 1 (2011): 30–32. http://dx.doi.org/10.1007/s11750-011-0230-8.

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