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Journal articles on the topic 'Linear complementarity problem'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Ames, W. F., and C. Brezinski. "The linear complementarity problem." Mathematics and Computers in Simulation 34, no. 2 (1992): 188–89. http://dx.doi.org/10.1016/0378-4754(92)90066-p.

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2

Brigden, M. E., R. W. Cottle, J. S. Pang, and R. E. Stone. "The Linear Complementarity Problem." Journal of the Royal Statistical Society. Series A (Statistics in Society) 156, no. 1 (1993): 125. http://dx.doi.org/10.2307/2982870.

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3

Anderson, E. J., and M. Aramendia. "Continuous linear complementarity problem." Journal of Optimization Theory and Applications 77, no. 2 (1993): 233–56. http://dx.doi.org/10.1007/bf00940711.

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4

Jenifer, D. H., and R. Irene Hepzibah. "On Solving Linear Complementarity Problem using Principal Pivoting Method." Indian Journal Of Science And Technology 17, no. 47 (2024): 4993–98. https://doi.org/10.17485/ijst/v17i47.3095.

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Objectives: A rudimentary framework called the linear complementarity problem (LCP) describes a wide range of real-world scenarios in which equilibrium conditions must be met while adhering to constraints. Methods: This study presents the Principal Pivoting Method (PPM), a novel method for solving linear Complementarity problems. PPM is a viable substitute for addressing large-scale complementarity problems. It is a powerful method for handling large-scale challenge circumstances while addressing LCPs. The PPM uses a principle-based pivoting strategy to navigate the solution space. It terminat

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5

Pardalos, Panos M., and Anna Nagurney. "The integer linear complementarity problem." International Journal of Computer Mathematics 31, no. 3-4 (1990): 205–14. http://dx.doi.org/10.1080/00207169008803803.

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6

De Schutter, Bart, and Bart De Moor. "The extended linear complementarity problem." Mathematical Programming 71, no. 3 (1995): 289–325. http://dx.doi.org/10.1007/bf01590958.

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7

Borwein, J. M., and M. A. H. Dempster. "The Linear Order Complementarity Problem." Mathematics of Operations Research 14, no. 3 (1989): 534–58. http://dx.doi.org/10.1287/moor.14.3.534.

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8

Mangasarian, O. L., and J. S. Pang. "The Extended Linear Complementarity Problem." SIAM Journal on Matrix Analysis and Applications 16, no. 2 (1995): 359–68. http://dx.doi.org/10.1137/s0895479893262734.

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9

Jenifer D H. "A Methodology for Solving Fuzzy Linear Programming Problem as a Fuzzy Linear Complementarity Problem." Communications on Applied Nonlinear Analysis 31, no. 2s (2024): 01–08. http://dx.doi.org/10.52783/cana.v31.587.

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In this paper, the linear complementarity problem with Fuzzy parameters is discussed. The Linear Programming Problem can be transformed into a Linear Complementarity Problem. The Maximum Index method is used to solve the converted Linear programming problem. The maximum index method has been introduced as a potential approach for identifying a complementarity feasible solution to the Linear Complementarity Problem. The fuzzy arithmetic operations are utilized for the triangular fuzzy numbers. A real-life example has been provided to demonstrate the suggested approach.

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10

Shmyrev, Vadim. "Polyhedral complementarity problem with quasimonotone decreasing mappings." Yugoslav Journal of Operations Research, no. 00 (2022): 31. http://dx.doi.org/10.2298/yjor2111016031s.

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The fixed point problem of piecewise constant mappings in Rn is investigated. This is a polyhedral complementarity problem, which is a generalization of the linear complementarity problem. Such mappings arose in the author?s research on the problem of economic equilibrium in exchange models, where mappings were considered on the price simplex. The author proposed an original approach of polyhedral complementarity, which made it possible to obtain simple algorithms for solving the problem. The present study is a generalization of linear complementarity methods to related problems of a more gene

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11

Li, Yuan, Hai-Shan Han, and Dan-Dan Yang. "A Penalized-Equation-Based Generalized Newton Method for Solving Absolute-Value Linear Complementarity Problems." Journal of Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/560578.

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We consider a class of absolute-value linear complementarity problems. We propose a new approximation reformulation of absolute value linear complementarity problems by using a nonlinear penalized equation. Based on this approximation reformulation, a penalized-equation-based generalized Newton method is proposed for solving the absolute value linear complementary problem. We show that the proposed method is globally and superlinearly convergent when the matrix of complementarity problems is positive definite and its singular values exceed 1. Numerical results show that our proposed method is

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12

Schutter, Bart De, and Bart De Moor. "The Linear Dynamic Complementarity Problem is a special case of the Extended Linear Complementarity Problem." Systems & Control Letters 34, no. 1-2 (1998): 63–75. http://dx.doi.org/10.1016/s0167-6911(97)00136-9.

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13

CHANDRASHEKARAN, A., T. PARTHASARATHY, and V. VETRIVEL. "SOLVING STRONGLY MONOTONE LINEAR COMPLEMENTARITY PROBLEMS." International Game Theory Review 15, no. 04 (2013): 1340035. http://dx.doi.org/10.1142/s0219198913400355.

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Given a linear transformation L on a finite dimensional real inner product space V to itself and an element q ∈ V we consider the general linear complementarity problem LCP (L, K, q) on a proper cone K ⊆ V. We observe that the iterates generated by any closed algorithmic map will converge to a solution for LCP (L, K, q), whenever L is strongly monotone. Lipschitz constants of L is vital in establishing the above said convergence. Hence we compute the Lipschitz constants for certain classes of Lyapunov, Stein and double-sided multiplicative transformations in the setting of semidefinite linear

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14

Sudha, N., R. Irene Hepzibah, and A. Nagoorgani. "On solving neutrosophic linear complementarity problem." Bulletin of Pure & Applied Sciences- Mathematics and Statistics 38e, no. 1 (2019): 336. http://dx.doi.org/10.5958/2320-3226.2019.00035.3.

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15

Yong, Long Quan. "Linear Complementarity Problem and Multiobjective Optimization." Applied Mechanics and Materials 101-102 (September 2011): 236–39. http://dx.doi.org/10.4028/www.scientific.net/amm.101-102.236.

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A new method is proposed for the linear complementarity problem (LCP). Firstly we formulate the LCP into a multiobjective optimization problem (MOP), and study the relations between the efficient solution of MOP and optimal solution of LCP. Based on the efficient solution of MOP, we define zero-efficient solution. Then we indicate that zero-efficient solution of the MOP is also the solution to the LCP. Finally some standard LCP examples are respectively transformed into MOP and solved by minimax method. Numerical results indicate that the proposed method is effective.

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16

Ferris, M. C. "Book Review: The linear complementarity problem." Bulletin of the American Mathematical Society 28, no. 1 (1993): 169–76. http://dx.doi.org/10.1090/s0273-0979-1993-00344-6.

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17

Danao, R. A. "On the Parametric Linear Complementarity Problem." Journal of Optimization Theory and Applications 95, no. 2 (1997): 445–54. http://dx.doi.org/10.1023/a:1022699624785.

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18

Chandrasekaran, R., S. N. Kabadi, and R. Sridhar. "Integer Solution for Linear Complementarity Problem." Mathematics of Operations Research 23, no. 2 (1998): 390–402. http://dx.doi.org/10.1287/moor.23.2.390.

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19

Zhenghai, Huang, and Li Xia. "Linear complementarity problem over tensor spaces." SCIENTIA SINICA Mathematica 50, no. 9 (2020): 1169. http://dx.doi.org/10.1360/ssm-2020-0050.

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20

Gowda, M. Seetharama, and Roman Sznajder. "The Generalized Order Linear Complementarity Problem." SIAM Journal on Matrix Analysis and Applications 15, no. 3 (1994): 779–95. http://dx.doi.org/10.1137/s0895479892237859.

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21

Mohan, S. R., S. K. Neogy, and R. Sridhar. "The generalized linear complementarity problem revisited." Mathematical Programming 74, no. 2 (1996): 197–218. http://dx.doi.org/10.1007/bf02592211.

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22

Gowda, M. Seetharama. "On the extended linear complementarity problem." Mathematical Programming 72, no. 1 (1996): 33–50. http://dx.doi.org/10.1007/bf02592330.

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23

Lüthi, Hans-Jakob. "Linear complementarity problem with upper bounds." European Journal of Operational Research 40, no. 3 (1989): 337–43. http://dx.doi.org/10.1016/0377-2217(89)90426-8.

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24

Bhatia, D., and Pankaj Gupta. "Generallized Linear Complementarity Problem and Multiobjective Programming Problem." Optimization 46, no. 2 (1999): 199–214. http://dx.doi.org/10.1080/02331939908844452.

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25

Gan, Mengting, and Gaoyan Yan. "Global Error Bounds for the Extended Vertical LCP of DZ matrices and DZ-B maxtrices." Journal of Physics: Conference Series 2890, no. 1 (2024): 012015. http://dx.doi.org/10.1088/1742-6596/2890/1/012015.

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Abstract The linear complementarity problem is a mathematical problem with important theoretical value and wide practical applications. Research on linear complementarity problems mainly focuses on algorithm improvement and innovation; Combining with fields such as machine learning and artificial intelligence to expand the application scope of linear complementarity problems; Further research on the properties of linear complementarity problems, the existence and uniqueness of solutions, and other theoretical issues. In this paper, by virtue of the properties of DZ-matrices and DZ-B matrices,

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26

Yong, Long Quan. "Solving Obstacle Problem Based on Potential-Reduction Interior Point Algorithm." Applied Mechanics and Materials 29-32 (August 2010): 725–31. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.725.

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This text studies a kind of obstacle problem. Combining with difference principle, we transform the original problem into monotone linear complementarity problem, and propose a novel method called potential-reduction interior point algorithm for monotone linear complementarity problem. We establish global and finite convergence of the new method. The reliability and efficiency of the algorithm is demonstrated by the numerical experiments of standard linear complementarity problems and the examples of obstacle problem with free boundary.

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27

Kwak, B. M. "Complementarity Problem Formulation of Three-Dimensional Frictional Contact." Journal of Applied Mechanics 58, no. 1 (1991): 134–40. http://dx.doi.org/10.1115/1.2897140.

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A general three-dimensional frictional contact problem has been formulated in the form of a complementarity problem in an incremental analysis setting. The derivation is straight forward and very natural. It is shown that the complementarity problem for a three-dimensional case is inherently nonlinear, not like the two-dimensional problem where a linear complementarity problem formulation is possible. The two-dimensional case is a special case of the three-dimensional formulation. Approximate linear complementarity problems of the nonlinear complementarity problem by a Newton approach, or by i

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28

Parida, J., A. Sen, and A. Kumar. "A linear complementarity problem involving a subgradient." Bulletin of the Australian Mathematical Society 37, no. 3 (1988): 345–51. http://dx.doi.org/10.1017/s0004972700026964.

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A linear complementarity problem, involving a given square matrix and vector, is generalised by including an element of the subdifferential of a convex function. The existence of a solution to this nonlinear complementarity problem is shown, under various conditions on the matrix. An application to convex nonlinear nondifferentiable programs is presented.

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29

Zhang, Li Pu, and Ying Hong Xu. "An Efficient Algorithm for Linear Complementarity Problems." Advanced Materials Research 204-210 (February 2011): 687–90. http://dx.doi.org/10.4028/www.scientific.net/amr.204-210.687.

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Through some modifications on the classical-Newton direction, we obtain a new searching direction for monotone horizontal linear complementarity problem. By taking the step size along this direction as one, we set up a full-step primal-dual interior-point algorithm for monotone horizontal linear complementarity problem. The complexity bound for the algorithm is derived, which is the best-known for linear complementarity problem.

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30

Lesaja, Goran. "Long step homogeneous interior point algorithm for the p* nonlinear complementarity problems." Yugoslav Journal of Operations Research 12, no. 1 (2002): 17–48. http://dx.doi.org/10.2298/yjor0201017l.

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A P*-Nonlinear Complementarity Problem as a generalization of the P*-Linear Complementarity Problem is considered. We show that the long-step version of the homogeneous self-dual interior-point algorithm could be used to solve such a problem. The algorithm achieves linear global convergence and quadratic local convergence under the following assumptions: the function satisfies a modified scaled Lipschitz condition, the problem has a strictly complementary solution, and certain submatrix of the Jacobian is nonsingular on some compact set.

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31

Yuan, Dongjin, and Hui Zhang. "Generalized AOR Algorithms for Linear Complementarity Problem." Journal of Algorithms & Computational Technology 1, no. 2 (2007): 187–200. http://dx.doi.org/10.1260/174830107781389030.

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32

Samir, Neogy, Sinha Sagnik, Das Arup, and Gupta Abhijit. "Scarf’s generalization of linear complementarity problem revisited." Yugoslav Journal of Operations Research 23, no. 2 (2013): 143–61. http://dx.doi.org/10.2298/yjor130203026n.

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33

Kappel, Nicholas W., and Layne T. Watson. "Iterative algorithms for the linear complementarity problem." International Journal of Computer Mathematics 19, no. 3-4 (1986): 273–97. http://dx.doi.org/10.1080/00207168608803522.

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34

Yuan, Dongjin, and Yongzhong Song. "Modified AOR methods for linear complementarity problem." Applied Mathematics and Computation 140, no. 1 (2003): 53–67. http://dx.doi.org/10.1016/s0096-3003(02)00194-7.

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35

Watson, Layne T., J. Patrick Bixler, and Aubrey B. Poore. "Continuous Homotopies for the Linear Complementarity Problem." SIAM Journal on Matrix Analysis and Applications 10, no. 2 (1989): 259–77. http://dx.doi.org/10.1137/0610020.

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36

Cao, Menglin, and Michael C. Ferris. "Pc-matrices and the linear complementarity problem." Linear Algebra and its Applications 246 (October 1996): 299–312. http://dx.doi.org/10.1016/0024-3795(94)00362-9.

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37

Xiao, Baichun, and Patrick T. Harker. "Perturbation results for the linear complementarity problem." Applied Mathematics Letters 2, no. 4 (1989): 401–5. http://dx.doi.org/10.1016/0893-9659(89)90098-0.

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38

Cottle, R. W., J. S. Pang, and V. Venkateswaran. "Sufficient matrices and the linear complementarity problem." Linear Algebra and its Applications 114-115 (March 1989): 231–49. http://dx.doi.org/10.1016/0024-3795(89)90463-1.

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39

Wu, Xian-Ping, and Ri-Huan Ke. "Backward errors of the linear complementarity problem." Numerical Algorithms 83, no. 3 (2019): 1249–57. http://dx.doi.org/10.1007/s11075-019-00723-9.

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40

Li, Yaotang, and Pingfan Dai. "Generalized AOR methods for linear complementarity problem." Applied Mathematics and Computation 188, no. 1 (2007): 7–18. http://dx.doi.org/10.1016/j.amc.2006.09.067.

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41

Flores-Bazán, Fabián, and Ruben López. "The Linear Complementarity Problem Under Asymptotic Analysis." Mathematics of Operations Research 30, no. 1 (2005): 73–90. http://dx.doi.org/10.1287/moor.1040.0110.

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42

Chung, S. J. "NP-Completeness of the linear complementarity problem." Journal of Optimization Theory and Applications 60, no. 3 (1989): 393–99. http://dx.doi.org/10.1007/bf00940344.

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43

Zakia, Kebbiche, and Roumili Hayet. "Combined approach to solve linear complementarity problem." Journal of Numerical Analysis and Approximation Theory 45, no. 2 (2016): 163–76. http://dx.doi.org/10.33993/jnaat452-1088.

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In this paper, we present a new approach in order to solve the linear complementary problem noted (LCP). We have combined the ideas of Lemke's method and its variants taking advantage of the benefits of each approach in order to improve the convergence of these algorithms.Numerical simulations and comparative results of the new approach are provided.Since the quadratic convex program and linear program can be written as (LCP), so it can be resolved thanks to our new approach.

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44

LI, LEI. "The Smallest Computational Complexity for the Linear Complementarity Problem with P-Matrix." Information 27, no. 4 (2024): 221–30. https://doi.org/10.47880/inf2704-01.

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The linear complementarity problem LCP(A, q) which consists of finding an real vector z such that Az+q>=0, z>=0, and z^T(Az+q)=0, where A and q are given real matrix and real vector respectively. When A is a P-matrix, LCP(A, q) is a NP-complete problem. Some traditional direct methods for solving the above problem need O(2^n n^2) or O(2^n n^3) number of arithmetic operations at least. This paper proposes a recursive algorithm for solving the LCP(A,q) with A is a P-matrix. The maximum computational complexity for proposed algorithm is not more than 0(2^n) which is the possible smallest co

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45

Jenifer D H. "An Interval approach to solve Fuzzy Fractional Programming Problem as a Fuzzy Linear Complementarity Problem." Communications on Applied Nonlinear Analysis 32, no. 5s (2024): 353–60. https://doi.org/10.52783/cana.v32.3106.

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An optimization problem where the goal function is a proportion between two functions is known as fractional programming, and the goal is to maximize or minimize the ratio. This paper discusses a methodology to resolve Fuzzy Fractional Programming Problem as a Fuzzy Linear Complementarity Problem. The study seeks to emphasize the key characteristics, make some new observation and motivate further application in linear complementarity problem. The constraints of the Fractional Programming problem is taken as a Fuzzy Linear Programming problem and further it transformed in to Fuzzy Linear Comple

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46

Foul, A. "Complementary irreducibilityS– matrices with connections to solutions of the linear complementarity problem." Optimization 36, no. 1 (1996): 25–30. http://dx.doi.org/10.1080/02331939608844162.

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47

D, H. Jenifer, and Irene Hepzibah R. "On Solving Linear Complementarity Problem using Principal Pivoting Method." Indian Journal of Science and Technology 17, no. 47 (2024): 4993–98. https://doi.org/10.17485/IJST/v17i47.3095.

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Abstract <strong>Objectives:</strong> A rudimentary framework called the linear complementarity problem (LCP) describes a wide range of real-world scenarios in which equilibrium conditions must be met while adhering to constraints. <strong>Methods:</strong> This study presents the Principal Pivoting Method (PPM), a novel method for solving linear Complementarity problems. PPM is a viable substitute for addressing large-scale complementarity problems. It is a powerful method for handling large-scale challenge circumstances while addressing LCPs. The PPM uses a principle-based piv

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48

Haddad, Caroline N., and George J. Habetler. "Projective algorithms for solving complementarity problems." International Journal of Mathematics and Mathematical Sciences 29, no. 2 (2002): 99–113. http://dx.doi.org/10.1155/s0161171202007056.

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We present robust projective algorithms of the von Neumann type for the linear complementarity problem and for the generalized linear complementarity problem. The methods, an extension of Projections Onto Convex Sets (POCS) are applied to a class of problems consisting of finding the intersection of closed nonconvex sets. We give conditions under which convergence occurs (always in2dimensions, and in practice, in higher dimensions) when the matrices areP-matrices (though not necessarily symmetric or positive definite). We provide numerical results with comparisons to Projective Successive Over

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49

Tian, Panjie, Zhensheng Yu, and Yue Yuan. "A smoothing Levenberg-Marquardt algorithm for linear weighted complementarity problem." AIMS Mathematics 8, no. 4 (2023): 9862–76. http://dx.doi.org/10.3934/math.2023498.

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<abstract> <p>In this paper, we consider the solution of linear weighted complementarity problem (denoted by LWCP). Firstly, we introduce a new class of weighted complementary functions and show that its continuously differentiable. On this basis, the LWCP is reconstructed as a smooth system of equations, and then solved by the Levenberg-Marquardt method. The convergence of the algorithm is proved theoretically and numerical experiments are carried out. The comparative experiments show that the algorithm has some advantages in computing time and iteration times.</p> </abst

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50

Darvay, Zsolt, and Ágnes Füstös. "Numerical Results for the General Linear Complementarity Problem." Műszaki Tudományos Közlemények 11, no. 1 (2019): 43–46. http://dx.doi.org/10.33894/mtk-2019.11.07.

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Abstract In this article we discuss the interior-point algorithm for the general complementarity problems (LCP) introduced by Tibor Illés, Marianna Nagy and Tamás Terlaky. Moreover, we present a various set of numerical results with the help of a code implemented in the C++ programming language. These results support the efficiency of the algorithm for both monotone and sufficient LCPs.

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