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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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01 Jan 2006
TL;DR: In this article, the nonlinear complementarity problems were converted to an equivalent smooth nonlinear equation system by using smoothing technique and then the Levenberg-Marquardt type method was used to solve the nonsingular Jacobian.
Abstract: In this paper, we convert the nonlinear complementarity problems to an equivalent smooth nonlinear equation system by using smoothing technique. Then we use Levenberg–Marquardt type method to solve the nonlinear equation system. The method has the following merits: (i) any cluster point of the iteration sequence is a solution of the P0 � NCP; (ii) it generates a bounded sequence if the P0 � NCP has a nonempty and bounded solution set; (iii) if the generalized Jacobian is nonsingular at a solution point, then the whole sequence converges to the (unique) solution of the P0 � NCP superlinearly; (iv) for the P0 � NCP, if an accumulation point of the iteration sequence satisfies strict complementary condition, then the whole sequence converges to this accumulation point superlinearly.
23 Sep 2011
TL;DR: In this article, a systematic approach for modeling power electronics converters is shown, referred as the Complementarity Framework, which allows to calculate the transient and steady state responses, and can be operated in the Discontinuous Operation Mode (DCM) and the Continuous operation Mode (CCM).
Abstract: In this paper, a systematic approach for modelling power electronics converters is shown, it is referred as the Complementarity Framework. The Complementarity Framework allows to calculate the transient and steady state responses. The single- phase diode bridge rectifier and the half-wave diode rectifier are modeled as Linear Complementarity Systems (LCS).The complementarity models can be operated in the Discontinuous Operation Mode (DCM) and the Continuous Operation Mode (CCM).
Cites methods from "Linear complementarity, linear and ..."
...The linear complementarity problem can be solved using Lemkes algorithm [13], PATH [14], and Quadratic Programing [15]....
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...Due to the low order of the complementarity model discussed in this paper, a standard Matlab code has been used [15]....
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TL;DR: In this paper, the modulus-based matrix splitting iteration method for solving a class of nonlinear complementarity problems under a weakened condition is discussed, and the general convergence conditions for the method in terms of spectral radius and matrix norm are presented.
Abstract: In this paper, we discuss the modulus-based matrix splitting iteration method for solving a class of nonlinear complementarity problems under a weakened condition, and present the general convergence conditions for the method in terms of spectral radius and matrix norm, respectively. Moreover, for some special cases of the method, we propose the concrete convergence conditions and optimal parameters. These convergence theories improve the existing results to some extent. The numerical experiments verify the validity and practicality of the presented results.
01 Jan 2006
TL;DR: In this article, a sign-solvable linear complementarity problem (LCP) with nonzero diagonals is shown to be solvable in polynomial time, where γ is the number of nonzero coefficients.
Abstract: This paper presents a connection between qualitative matrix theory and linear complemen-tarity problems(LCPs). An LCP is said to be sign-solvable if the set of the sign patterns of thesolutions is uniquely determined by the sign patterns of the given coefficients. We provide acharacterization for sign-solvable LCPs such that the coefficient matrix has nonzero diagonals,which can be tested in polynomial time. This characterization leads to an efficient combina-torial algorithm to find the sign pattern of a solution for these LCPs. The algorithm runs inO( γ ) time, where γ is the number of the nonzero coefficients.Key Words: Linear Complementarity Problems, Combinatorial Matrix Theory 1 Introduction This paper deals with linear complementarity problems(LCPs) in the following form:LCP( A,b ): find ( w,z )s.t. w = Az + b,w T z = 0 ,w ≥ 0 , z ≥ 0 , where A is a real square matrix, and b is a real vector. The LCP, introduced by Cottle[4], Cottle andDantzig[5], and Lemke[16], is one of the most widely studied mathematical programming problems,which contains linear programming and convex quadratic programming. Solving LCP(
01 Jan 2003
TL;DR: This study presents a new parallel iterative method to solve the estimation problem in an ∞ norm, a parallel version of Dax's algorithm that is a row-relaxation type which is a convenient when the system to be solved is inconsistent, large, sparse and unstructured.
Abstract: This study presents a new parallel iterative method to solve the estimation problem in an ∞ norm. This algorithm, a parallel version of Dax’s algorithm, is a row-relaxation type which is a convenient when the system to be solved is inconsistent, large, sparse and unstructured.
Additional excerpts
...Exemplo 3: ( Murty, 1988, p.19) A é uma matriz n x n, onde i > j a = b e i j i = j = a n j= ijiij se2 se0 se1 1 para , m, , i = 21 ....
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