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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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Proceedings Article
14 Dec 2009
TL;DR: In this paper, the problem of finding the independent number of an undirected graph is formulated as two equivalent Mathematical Programs with Linear Complementarity Constraints (MPLCC).
Abstract: The problem of finding the independent number of an undirected graph is formulated as two equivalent Mathematical Programs with Linear Complementarity Constraints (MPLCC). A multistarting Lemke's method is introduced for dealing with the first formulation and is able to find a good approximate of the independent number in a finite number of iterations. A sequential complementary algorithm is also discussed for the second formulation and can find the independent number at least in theory. Some computational experience is included to highlight the efficacy of the complementary approaches for computing the independent number of graphs from the Dimacs collection.
01 Jan 2013
TL;DR: A new method for solving bimatrix game with triangular fuzzy numbers using LCP has been applied and the obtained solution is the solution of the given fuzzy bim atrix game.
Abstract: A method for the two person non-zero sum game whose payoffs are represented by interval data has been investigated. In this paper a new method for solving bimatrix game with triangular fuzzy numbers using LCP has been applied. The obtained solution of this FLCP is the solution of the given fuzzy bimatrix game.
Proceedings ArticleDOI
01 Dec 2017
TL;DR: The paper addresses the problem of finding a new valid model structure as a process within the discrete phase ofEquation-based 1 modelling of hybrid systems and the usage of the Linear Complementarity Problem (LCP).
Abstract: Equation-based 1 modelling of hybrid systems has to consider dynamical systems consisting of components with continuous and/or discrete behavior. The paper focuses on such systems under special consideration of systems with variable model structure. Some ideas are presented how a simulation of continuous and discrete phenomena can be handled correctly. The main process is a continuing alternation between continuous and discrete simulation phases, where in the discrete phase the changeover can be performed to a new model structure which is valid during the next continuous phase. The paper addresses the problem of finding a new valid model structure as a process within the discrete phase. This new valid model structure has to be found under consideration of the time history of the model's variables within the preceding continuous phase. To this end, the usage of the Linear Complementarity Problem (LCP) is proposed. After a definition of hybrid systems and the term model structure, different types of events - with and without influence on the model structure - are listed and properties of complementarity are presented. To find the correct switchover from continuous to discrete phase, so-called indicator functions are used. On the contrary, to find the correct switchover from discrete to continuous phase, the LCP is applied. Some simulation results for an electromechanical system are briefly presented.

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

  • ...Another solution algorithm – a complementary Pivot algorithm – was proposed in [52] and is also described in [53] and [54]....

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Posted Content
TL;DR: In this article, the posterior probability of a convex function that goes through the true function values at the design points is estimated using Monte Carlo simulation, and three variance reduction methods are proposed: change of measure, acceptance-rejection, and conditional Monte Carlo.
Abstract: Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function values at the design points. We develop an asymptotically consistent Bayesian sequential sampling procedure that estimates the posterior probability of this being true. In each iteration, the posterior probability is estimated using Monte Carlo simulation. We offer three variance reduction methods -- change of measure, acceptance-rejection, and conditional Monte Carlo. Numerical experiments suggest that the conditional Monte Carlo method should be preferred.