On the Global Solution of Linear Programs with Linear Complementarity Constraints

Jing Hu, John E. Mitchell, Jong‐Shi Pang, Kristin P. Bennett, Gautam Kunapuli

Type: Article

Publication Date: 2008-01-01

Citations: 101

DOI: https://doi.org/10.1137/07068463x

View

Locations

SIAM Journal on Optimization - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	A graphical framework for global optimization of mixed-integer nonlinear programs	2024	Danial Davarnia Mohammadreza Kiaghadi
+	Global Resolution of Convex Programs with Complementarity Constraints	2011	John E. Mitchell Jong‐Shi Pang
+ PDF Chat	Globally Solving Nonconvex Quadratic Programs via Linear Integer Programming Techniques	2019	Wei Xia Juan C. Vera Luis F. Zuluaga
+	Global Resolution of Convex Programs with Complementarity Constraints	2011	John Mitchell Jong‐Shi Pang
+ PDF Chat	SDP-quality bounds via convex quadratic relaxations for global optimization of mixed-integer quadratic programs	2021	Carlos J. Nohra Arvind U. Raghunathan Nikolaos V. Sahinidis
+	SDP-quality bounds via convex quadratic relaxations for global optimization of mixed-integer quadratic programs	2021	Carlos J. Nohra Arvind U. Raghunathan Nikolaos V. Sahinidis
+	SDP-quality bounds via convex quadratic relaxations for global optimization of mixed-integer quadratic programs	2021	Carlos J. Nohra Arvind U. Raghunathan Nikolaos V. Sahinidis
+	Novel Relaxation Techniques for Global Optimization of NLPs and MINLPs	2020	Nohra Khouri Jose Carlos
+	Obtaining Tighter Relaxations of Mathematical Programs with Complementarity Constraints	2012	John E. Mitchell Jong‐Shi Pang Bin Yu
+	Solving Linear Programs with Complementarity Constraints using Branch-and-Cut	2018	Bin Yu John E. Mitchell Jong‐Shi Pang
+	Globally solving Non-Convex Quadratic Programs via Linear Integer Programming techniques	2015	Wei Xia Juan C. Vera Luis F. Zuluaga
+ PDF Chat	Solving linear programs with complementarity constraints using branch-and-cut	2018	Bin Yu John E. Mitchell Jong‐Shi Pang
+	New Characterizations and Efficient Local Search for General Integer Linear Programming	2023	Peng Lin Shaowei Cai Mengchuan Zou Jinkun Lin
+	Global Solutions of Nonconvex Standard Quadratic Programs via Mixed Integer Linear Programming Reformulations	2018	Jacek Gondzio Esma Yildirim
+	Global Solutions of Nonconvex Standard Quadratic Programs via Mixed Integer Linear Programming Reformulations	2018	Jacek Gondzio E. Alper Yıldırım
+ PDF Chat	A review of algorithmic enhancements for Benders decomposition	2016	Halil Şen Boris Detienne Ruslan Sadykov François Vanderbeck
+	A Penalty Branch-and-Bound Method for Mixed Binary Linear Complementarity Problems	2022	Marianna De Santis Sven de Vries Martin Schmidt Lukas Winkel
+	SCIP: global optimization of mixed-integer nonlinear programs in a branch-and-cut framework	2017	Stefan Vigerske Ambros Gleixner
+	Scylla: a matrix-free fix-propagate-and-project heuristic for mixed-integer optimization	2023	Gioni Mexi Mathieu Besançon Suresh Bolusani Antonia Chmiela Ambros Gleixner Alexander Hoen
+	Relaxations and cutting planes for linear programs with complementarity constraints	2024	Alberto Del Pia Jeff Linderoth Haoran Zhu

Cited by (47)

Action	Title	Year	Authors
+	On conic QPCCs, conic QCQPs and completely positive programs	2015	Lijie Bai John E. Mitchell Jong‐Shi Pang
+	A Globally Convergent Filter Method for MPECs	2007	Sven Leyffer Todd Munson
+ PDF Chat	OPTIMIZATION WITH LINEAR COMPLEMENTARITY CONSTRAINTS	2014	Joaquím J. Júdice
+	Branch-and-bound algorithms for the partial inverse mixed integer linear programming problem	2013	Lizhi Wang
+ PDF Chat	How to convexify the intersection of a second order cone and a nonconvex quadratic	2016	Samuel Burer Fatma Kılınç-Karzan
+ PDF Chat	Beyond Canonical DC-Optimization: The Single Reverse Polar Problem	2012	Giancarlo Bigi Antonio Frangioni Qinghua Zhang
+ PDF Chat	Global solutions of nonconvex standard quadratic programs via mixed integer linear programming reformulations	2021	Jacek Gondzio E. Alper Yıldırım
+	An LPCC approach to nonconvex quadratic programs	2010	Jing Hu John E. Mitchell Jong‐Shi Pang
+	A Globally Convergent Probability-One Homotopy for Linear Programs with Linear Complementarity Constraints	2013	Layne T. Watson Stephen C. Billups John E. Mitchell David R. Easterling
+	Three essays on multi-level optimization models and applications	2016	Mohammad Hosseini Rahdar
+	Modeling Mathematical Programs with Equilibrium Constraints in Pyomo	2015	William Hart John Daniel Siirola
+ PDF Chat	On linear problems with complementarity constraints	2022	Giandomenico Mastroeni Letizia Pellegrini Alberto Peretti
+	Conic approximation to quadratic optimization with linear complementarity constraints	2016	Jing Zhou Shu‐Cherng Fang Wenxun Xing
+ PDF Chat	Globally solving quadratic programs with convex objective and complementarity constraints via completely positive programming	2017	Zhibin Deng Ye Tian Cheng Lü Wenxun Xing
+ PDF Chat	Inverse Optimization: Theory and Applications	2023	Timothy C. Y. Chan Rafid Mahmood Ian Yihang Zhu
+	Implicit solution function of P0 and Z matrix linear complementarity constraints	2009	Xiaojun Chen Shuhuang Xiang
+ PDF Chat	Cardinality Minimization, Constraints, and Regularization: A Survey	2024	Andreas M. Tillmann Daniel Bienstock Andrea Lodi Alexandra Schwartz
+ PDF Chat	Sequential Linearization Method for Bound-Constrained Mathematical Programs with Complementarity Constraints	2022	Christian Kirches Jeffrey Larson Sven Leyffer Paul Manns
+	A branch and cut approach to linear programs with linear complementarity constraints	2011	Bin Yu
+	Relaxations and cutting planes for linear programs with complementarity constraints	2024	Alberto Del Pia Jeff Linderoth Haoran Zhu
+	SOLVING TWO-LEVEL OPTIMIZATION PROBLEMS WITH APPLICATIONS TO ROBUST DESIGN AND ENERGY MARKETS	2011	Sauleh Siddiqui
+	A study of the difference-of-convex approach for solving linear programs with complementarity constraints	2017	Francisco Jara-Moroni Jong‐Shi Pang Andreas Wächter
+	An algorithm for global solution to bi-parametric linear complementarity constrained linear programs	2014	Yu‐Ching Lee Jong‐Shi Pang John E. Mitchell
+	How to Convexify the Intersection of a Second Order Cone and a Nonconvex Quadratic	2014	Sam Burer Fatma Kılınç-Karzan
+ PDF Chat	Convergence of Time-Stepping Schemes for Passive and Extended Linear Complementarity Systems	2009	Lanshan Han Alok Tiwari M. Kanat Camlibel Jong‐Shi Pang
+	MPEC Methods for Bilevel Optimization Problems	2020	Young‐Dae Kim Sven Leyffer Todd Munson
+	Obtaining Tighter Relaxations of Mathematical Programs with Complementarity Constraints	2012	John E. Mitchell Jong‐Shi Pang Bin Yu
+	Global resolution of the support vector machine regression parameters selection problem with LPCC	2015	Yu‐Ching Lee Jong‐Shi Pang John E. Mitchell
+	Convexification techniques for linear complementarity constraints	2021	Trang Nguyen Jean‐Philippe P. Richard Mohit Tawarmalani
+ PDF Chat	On the asymmetric eigenvalue complementarity problem	2009	Joaquím J. Júdice Hanif D. Sherali Isabel M. Ribeiro Silvério Rosa
+ PDF Chat	Solving linear programs with complementarity constraints using branch-and-cut	2018	Bin Yu John E. Mitchell Jong‐Shi Pang
+	On convex quadratic programs with linear complementarity constraints	2012	Lijie Bai John E. Mitchell Jong‐Shi Pang
+	A Class of Quadratic Programs with Linear Complementarity Constraints	2009	Xiaojun Chen Jane J. Ye
+	An Accelerated Dual Gradient-Projection Algorithm for Embedded Linear Model Predictive Control	2013	Panagiotis Patrinos Alberto Bemporad
+	Using quadratic convex reformulation to tighten the convex relaxation of a quadratic program with complementarity constraints	2013	Lijie Bai John E. Mitchell Jong‐Shi Pang
+	Three modeling paradigms in mathematical programming	2010	Jong‐Shi Pang
+	A branch-and-bound algorithm for instrumental variable quantile regression	2017	Guanglin Xu Samuel Burer
+	Global Solutions of Nonconvex Standard Quadratic Programs via Mixed Integer Linear Programming Reformulations	2018	Jacek Gondzio E. Alper Yıldırım
+	A pivoting algorithm for linear programming with linear complementarity constraints	2010	Haw‐ren Fang Sven Leyffer Todd Munson
+	Complementarity Formulations of ' 0 -norm Optimization Problems	2013	Mingbin Feng John E. Mitchell Jong‐Shi Pang Xin Shen

Citing (34)

Action	Title	Year	Authors
+	Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming	2002	Mohit Tawarmalani Nikolaos V. Sahinidis
+ PDF Chat	Complementarity constraints as nonlinear equations: Theory and numerical experience	2006	Sven Leyffer
+	None	2003	Houyuan Jiang Daniel Ralph
+	State of the art in global optimization: computational methods and applications	1996	Pãnos M. Pardalos Christodoulos A. Floudas
+ PDF Chat	Logic‐Based Methods for Optimization	2000	John Hooker
+	None	1999	Jong‐Shi Pang Masao Fukushima
+ PDF Chat	An Implementable Active-Set Algorithm for Computing a B-Stationary Point of a Mathematical Program with Linear Complementarity Constraints	2002	Masao Fukushima Paul Tseng
+	The Linear Complementarity Problem	2009	Richard W. Cottle Jong‐Shi Pang Richard Stone
+ PDF Chat	Convergence of a Penalty Method for Mathematical Programming with Complementarity Constraints	2004	Xiaohui Hu Daniel Ralph
+	Global Convergence of an Elastic Mode Approach for a Class of Mathematical Programs with Complementarity Constraints	2005	Mihai Anitescu
+	Solving mathematical programs with complementarity constraints as nonlinear programs	2004	R. Fletcher Sven Leyffer
+	Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity	2000	Holger Scheel Stefan Scholtes
+	Convergence Properties of a Regularization Scheme for Mathematical Programs with Complementarity Constraints	2001	Stefan Scholtes
+	On the Guignard constraint qualification for mathematical programs with equilibrium constraints	2005	Michael L. Flegel Christian Kanzow
+	A global optimization algorithm (GOP) for certain classes of nonconvex NLPs—I. Theory	1990	Christodoulos A. Floudas V. Visweswaran
+	Some Feasibility Issues in Mathematical Programs with Equilibrium Constraints	1998	Masao Fukushima Jong‐Shi Pang
+	On Using the Elastic Mode in Nonlinear Programming Approaches to Mathematical Programs with Complementarity Constraints	2005	Mihai Anitescu
+	New Branch-and-Bound Rules for Linear Bilevel Programming	1992	Pierre Hansen Brigitte Jaumard Gilles Savard
+	Optimality Conditions for a Class of Mathematical Programs with Equilibrium Constraints	1999	Jan Outrata
+	Constraint Qualifications and Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints	2000	Jane J. Ye
+ PDF Chat	Elastic-mode algorithms for mathematical programs with equilibrium constraints: global convergence and stationarity properties	2006	Mihai Anitescu Paul Tseng Stephen J. Wright
+	Primal-relaxed dual global optimization approach	1993	Christodoulos A. Floudas V. Visweswaran
+ PDF Chat	Interior Methods for Mathematical Programs with Complementarity Constraints	2006	Sven Leyffer Gabriel López-Calva Jorge Nocedal
+	Combinatorial Benders' Cuts for Mixed-Integer Linear Programming	2006	Gianni Codato Matteo Fischetti
+ PDF Chat	Some properties of regularization and penalization schemes for MPECs	2004	Daniel Ralph Stephen J. Wright
+	Classification model selection via bilevel programming	2008	Gautam Kunapuli Kristin P. Bennett Jing Hu Jong‐Shi Pang
+	Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints	2005	Jane J. Ye
+	Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints	1997	Jane J. Ye Xinrui Ye
+	Convergence of a Smoothing Continuation Method for Mathematical Progams with Complementarity Constraints	1999	Masao Fukushima Jong‐Shi Pang
+	Smooth SQP Methods for Mathematical Programs with Nonlinear Complementarity Constraints	2000	Houyuan Jiang Daniel Ralph
+	Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints	2006	R. Fletcher Sven Leyffer D. Ralph Stefan Scholtes
+	Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints	2003	Stephan Dempe
+	New Branch-and-Bound Rules for Linear Bilevel Programming.	1992	Pierre Hansen Brigitte Jaumard Gilles Savard
+ PDF Chat	On the global minimization of the value-at-risk	2004	Jong‐Shi Pang Sven Leyffer