Linear complementarity, linear and nonlinear programming

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Linear complementarity, linear and nonlinear programming

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Linear complementarity, linear and nonlinear programming

01 Jan 1988-

About: The article was published on 1988-01-01 and is currently open access. It has received 1012 citations till now. The article focuses on the topics: Mixed complementarity problem & Complementarity theory.

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Journal Article•DOI•

Study of a piecewise linear dynamic system with negative and positive stiffness

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Keguan Zou¹, Satish Nagarajaiah¹•Institutions (1)

Rice University¹

01 May 2015-Communications in Nonlinear Science and Numerical Simulation

TL;DR: A modified Lindstedt–Poincare method (modified L–P method) is adopted to derive approximate periodic solutions for the forced and damped system and its frequency-response curves are obtained through numerical simulation.

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25 citations

Cites methods from "Linear complementarity, linear and ..."

...The eventdriven algorithm [9] and algorithms for solving linear complementarity problems (LCP) [10] are widely used....
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...Figure 13 shows time history and phase portrait, which are obtained using an LCP solver based on time stepping method for µ̄ = 0.05, k̄ = −3.0, F̄ = 2.0, and Ω = 0.9....
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...13, 14, and 15, are obtained by using an LCP solver based on time stepping method....
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...The other is to obtain the time histories of the PWS system by using an LCP solver based on the time stepping method [10] in light of the fact that a PWS system is equivalent to an LCP....
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...It should be noted that all the numerical results in this section are obtained using an LCP solver based on the time stepping method....
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Journal Article•DOI•

Two characterizations of sufficient matrices

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Richard W. Cottle¹, Sy-Ming Guu¹•Institutions (1)

Stanford University¹

01 Jun 1992-Linear Algebra and its Applications

TL;DR: In this article, two characterizations for the class of sufficient matrices defined by Cottle, Pang, and Venkateswaran are given for linear programming terms.

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24 citations

Book•

Complementarity and Variational Inequalities in Electronics

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Khalid Addi¹, Daniel Goeleven¹•Institutions (1)

University of La Réunion¹

16 Jun 2017

TL;DR: The purpose of this chapter is to review and describe the main mathematical models applicable to the study of electrical networks involving devices like diodes whose Ampere–Volt characteristics are set-valued graphs.

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Abstract: The purpose of this chapter is to review and describe the main mathematical models applicable to the study of electrical networks involving devices like diodes whose Ampere–Volt characteristics are set-valued graphs. The mathematical models in question are related to complementarity problems, variational inequalities, and non-regular dynamical systems.

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24 citations

Journal Article•DOI•

The general two-sweep modulus-based matrix splitting iteration method for solving linear complementarity problems

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Huan Ren¹, Xiang Wang¹, Xiao-Bin Tang², Teng Wang¹•Institutions (2)

Nanchang University¹, Beijing Institute of Foreign Trade²

15 Feb 2019-Computers & Mathematics With Applications

TL;DR: Convergence analysis shows that the general two-sweep modulus-based matrix splitting iteration method will converge to the exact solution of linear complementarity problem under appropriate conditions.

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Abstract: In this paper, we present a general two-sweep modulus-based iteration method to solve a class of linear complementarity problems. Convergence analysis shows that the general two-sweep modulus-based matrix splitting iteration method will converge to the exact solution of linear complementarity problem under appropriate conditions. Numerical experiments further show that the proposed methods are superior to the existing methods in actual implementation.

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24 citations

Proceedings Article•DOI•

Extensive analysis of Linear Complementarity Problem (LCP) solver performance on randomly generated rigid body contact problems

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Evan Drumwright¹, Dylan A. Shell²•Institutions (2)

George Washington University¹, Texas A&M University²

24 Dec 2012

TL;DR: This paper undertakes the first comprehensive evaluation of LCP solvers across the space of multi-rigid body contact problems along the dimensions of solubility, solution quality, and running time.

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Abstract: The Linear Complementarity Problem (LCP) is a key problem in robot dynamics, optimization, and simulation. Common experience with dynamic robotic simulations suggests that the numerical robustness of the LCP solver often determines simulation usability: if the solver fails to find a solution or finds a solution with significant residual error, interpenetration can result, the simulation can gain energy, or both. This paper undertakes the first comprehensive evaluation of LCP solvers across the space of multi-rigid body contact problems. We evaluate the performance of these solvers along the dimensions of solubility, solution quality, and running time.

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24 citations