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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: A relaxation modulus-based matrix splitting iteration method is established, which covers the known general modulus based matrix splitting iterations methods and is efficient and accelerate the convergence performance with less iteration steps and CPU times.
Abstract: In this paper, a relaxation modulus-based matrix splitting iteration method is established, which covers the known general modulus-based matrix splitting iteration methods. The convergence analysis and the strategy of the choice of the parameters are given. Numerical examples show that the proposed methods are efficient and accelerate the convergence performance with less iteration steps and CPU times.
53 citations
Cites background from "Linear complementarity, linear and ..."
..., the economies with institutional restrictions upon prices, the linear and quadratic programming, the free boundary problems, and the optimal stopping in Markov chain; see [8, 16] for details....
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TL;DR: A semidefinite relaxation method based on a polynomial optimization model is presented so that all solutions of the tensor complementarity problem can be found under the assumption that the solution set of the problem is finite.
Abstract: This work, with its three parts, reviews the state-of-the-art of studies for the tensor complementarity problem and some related models. In the first part of this paper, we have reviewed the theoretical developments of the tensor complementarity problem and related models. In this second part, we review the developments of solution methods for the tensor complementarity problem. It has been shown that the tensor complementarity problem is equivalent to some known optimization problems, or related problems such as systems of tensor equations, systems of nonlinear equations, and nonlinear programming problems, under suitable assumptions. By solving these reformulated problems with the help of structures of the involved tensors, several numerical methods have been proposed so that a solution of the tensor complementarity problem can be found. Moreover, based on a polynomial optimization model, a semidefinite relaxation method is presented so that all solutions of the tensor complementarity problem can be found under the assumption that the solution set of the problem is finite. Further applications of the tensor complementarity problem will be given and discussed in the third part of this paper.
52 citations
TL;DR: A neural-network model for solving asymmetric linear variational inequalities is given, based on a simple projection and contraction method, for linear programming and linear complementarity problems.
Abstract: A linear variational inequality is a uniform approach for some important problems in optimization and equilibrium problems. We give a neural network model for solving asymmetric linear variational inequalities. The model is based on a simple projection and contraction method. Computer simulation is performed for linear programming (LP) and linear complementarity problems (LCP). The test results for the LP problem demonstrate that our model converges significantly faster than the three existing neural network models examined in a comparative study paper.
52 citations
Cites methods from "Linear complementarity, linear and ..."
...In addition, we report the simulation results by our proposed model for a set of asymmetric linear complementarity problems for which Lemke’s algorithm is known to run in exponential time [18]....
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TL;DR: The bilinear algorithm solved 80 consecutive cases of the LCP formulation of the knapsack feasibility problem, with almost constant average number of major iterations equal to four.
Abstract: The nonmonotone linear complementarity problem (LCP) is formulated as a bilinear program with separable constraints and an objective function that minimizes a natural error residual for the LCP. A linear-programming-based algorithm applied to the bilinear program terminates in a finite number of steps at a solution or stationary point of the problem. The bilinear algorithm solved 80 consecutive cases of the LCP formulation of the knapsack feasibility problem ranging in size between 10 and 3000, with almost constant average number of major iterations equal to four.
52 citations
TL;DR: In this paper, the most important research areas related to the energy market are classified based on critical research areas such as auction based pricing, bidding strategy formulation, market equilibria, and market power.
51 citations