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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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TL;DR: The modulus-based matrix splitting iteration methods, which are obtained by reformulating equivalently SDLCP as an implicit fixed-point matrix equation, are established.
Abstract: In this paper, we present some novel observations for the semidefinite linear complementarity problems, abbreviated as SDLCPs. Based on these new results, we establish the modulus-based matrix splitting iteration methods, which are obtained by reformulating equivalently SDLCP as an implicit fixed-point matrix equation. The convergence of the proposed modulus-based matrix splitting iteration methods has been analyzed. Numerical experiments have shown that the modulus-based iteration methods are effective for solving SDLCPs.
6 citations
Cites methods from "Linear complementarity, linear and ..."
...In 1988, Murty [33] presented a modulus iteration method for solving the following linear complementarity problem (LCP) [8, 12], for finding the vectors z ∈ Rn and w ∈ Rn such that z ∈ Rn+, w := Az + q ∈ Rn+ and 〈z, w〉 = 0, (1.2) which was by reformulating LCP as an implicit fixed-point equation....
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...In 1988, Murty [33] presented a modulus iteration method for solving the following linear complementarity problem (LCP) [8, 12], for finding the vectors z ∈ R and w ∈ R such that z ∈ Rn+, w := Az + q ∈ Rn+ and 〈z, w〉 = 0, (1....
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TL;DR: A method for handling soft constraints in situations where the decision-maker can associate a cost function with the ‘right-hand side’ values of these constraints that satisfies the usual economies of scale property of decreasing marginal costs is proposed.
Abstract: In this discussion we propose a method for handling soft constraints in situations where the decision-maker can associate a cost function with the ‘right-hand side’ values of these constraints that satisfies the usual economies of scale property of decreasing marginal costs. The method constitutes a natural application of composite concave programming, and seems to be particularly suited for situations where the underlying problem is of the linear/quadratic programming type.
6 citations
TL;DR: Chandrasekaran's algorithm for solving the linear complementarity problem with a Z-matrix is extended to solve the generalized linear complearity problem (GLCP) when the is a vertical block Zmatrix of type (m 1,…,m n).
Abstract: Chandrasekaran's algorithm for solving the linear complementarity problem with a Z-matrix is extended to solve the Generalized Linear Complementarity Problem (GLCP) when the is a vertical block Z-matrix of type (m 1,…,m n). The extended scheme solves the GLCP in at most n cycles by either finding a solution or declaring that none exists. Numerical examples are given to demonstrate the effectiveness of the algorithm
6 citations
TL;DR: In this paper, the general modulus Jacobi method and its convergence property were established, and the domain and the optimum value of the parameter were presented in one special situation, and numerical results show that this method is superior to some other modulus methods in computing efficiency and feasible aspects in some situations.
Abstract: For the large sparse linear complementarity problem, by reformulating them as implicit fixed-point equations problems, relying on matrix-splittings, many modulus methods are produced. In this paper, the general modulus Jacobi method and its convergence property were established, and the domain and the optimum value of the parameter are presented in one special situation. Numerical results show that this method is superior to some other modulus methods in computing efficiency and feasible aspects in some situations.
6 citations
TL;DR: In this paper, the convergence of the modulus-based successive overrelaxation method for the linear complementarity problem from discretization of Black-Scholes American option model is analyzed.
Abstract: We consider the modulus-based successive overrelaxation met- hod for the linear complementarity problems from the discretization of Black-Scholes American options model. The H+-matrix property of the system matrix discretized from American option pricing which guaran- tees the convergence of the proposed method for the linear complementar- ity problem is analyzed. Numerical experiments confirm the theoretical analysis, and further show that the modulus-based successive overrelax- ation method is superior to the classical projected successive overrelaxation method with optimal parameter.
6 citations
Cites methods from "Linear complementarity, linear and ..."
...For the convergence of these projected methods, we refer the reader to [14, 15]....
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