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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: This poster presents a probabilistic procedure to estimate the intensity of the response of the immune system to laser-spot assisted treatment of central nervous system injuries.
Abstract: Reference EPFL-ARTICLE-229257 URL: http://arxiv.org/abs/0903.4856 Record created on 2017-06-21, modified on 2017-06-21
10 citations
Cites background or methods from "Linear complementarity, linear and ..."
...We will show that a regularization approach to the analysis of preference data leads to a parameterized quadratic program with a sparse, low rank positive semi-definite matrix describing the quadratic term of the objective function....
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...The dual of the soft margin C-SVM is the following pQP (observe that the regularization parameter moves from the objective function to the constraints): maximizeα P i αi − 1 2 P i,j αiαjyiyjx T i xj subject to P i yiαi = 1 0 ≤ αi ≤ C (3)...
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01 Jan 2015
TL;DR: The resulting mixed integer optimization problems are tackled with a modern optimization algorithm, namely particle swarm optimization (PSO), as well as a hybrid scheme that combines PSO with the deterministic Active-Set optimization method.
Abstract: Graphical abstractDisplay Omitted HighlightsOptimal allocation of source and channel coding rates and power levels of nodes.Minimization of the average and maximum distortion of video received by all nodes.Mixed integer optimization problems.Mixed-integer optimization problems arise.The particle swarm optimization (PSO) algorithm is used.A hybrid algorithm that combines PSO and active set algorithm is used. Visual sensor networks (VSNs) consist of spatially distributed video cameras that are capable of compressing and transmitting the video sequences they acquire. We consider a direct-sequence code division multiple access (DS-CDMA) VSN, where each node has its individual requirements in compression bit rate and energy consumption, depending on the corresponding application and the characteristics of the monitored scene. We study two optimization criteria for the optimal allocation of the source and channel coding rates, which assume discrete values, as well as for the power levels of all nodes, which are continuous, under transmission bit rate constraints. The first criterion minimizes the average distortion of the video received by all nodes, while the second one minimizes the maximum video distortion among all nodes. The resulting mixed integer optimization problems are tackled with a modern optimization algorithm, namely particle swarm optimization (PSO), as well as a hybrid scheme that combines PSO with the deterministic Active-Set optimization method. Extensive experimentation on interference-limited as well as noisy environments offers significant intuition regarding the effectiveness of the considered optimization schemes, indicating the impact of the video sequence characteristics on the joint determination of the transmission parameters of the VSN.
10 citations
TL;DR: This work proves that the problem of computing an equilibrium in Arrow-Debreu markets with PLC utilities and PLC production sets is in the class FIXP, and provides dichotomies for equilibrium computation problems, both Nash and market.
Abstract: Piecewise-linear, concave (PLC) utility functions play an important role in work done at the intersection of economics and algorithms. We prove that the problem of computing an equilibrium in Arrow-Debreu markets with PLC utilities and PLC production sets is in the class FIXP. Recently it was shown that these problems are also FIXP-hard [21], hence settling the complexity of this long-standing open problem. Central to our proof is capturing equilibria of these markets as fixed points of a continuous function via a nonlinear complementarity problem (NCP) formulation. Next, we provide dichotomies for equilibrium computation problems, both Nash and market. There is a striking resemblance in the dichotomies for these two problems, hence providing a unifying view. We note that in the past, dichotomies have played a key role in bringing clarity to the complexity of decision and counting problems.
10 citations
TL;DR: In this paper, the authors describe all solutions of an n×n linear complementarity problem x+ = Mx−+q in terms of 2 n matrices and their Moore-Penrose inverses.
Abstract: Description of all solutions of an n×n linear complementarity problem x+ = Mx−+q in terms of 2 n matrices and their Moore-Penrose inverses is given. The result is applied to describe all solutions of the absolute value equation Ax + B|x| = b.
10 citations
Cites background from "Linear complementarity, linear and ..."
...The linear complementarity problem has been much studied in the last forty years, as evidenced in the monographs by Cottle, Pang and Stone [2], Murty [4] and Schäfer [7]....
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...[4] K. G. Murty....
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...The linear complementarity problem has been much studied in the last forty years, as evidenced in the monographs by Cottle, Pang and Stone [2], Murty [4] and Schäfer [7]....
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TL;DR: It is shown that the Euclidean norm appearing in the proximity function of the non-linear split feasibility problem can be replaced by arbitrary Bregman divergences, and the algorithm is based on the principle of majorization–minimization, is amenable to quasi-Newton acceleration, and comes complete with convergence guarantees under mild assumptions.
Abstract: The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range constraints. Split feasibility generalizes important inverse problems including convex feasibility, linear complementarity, and regression with constraint sets. When a feasible point does not exist, solution methods that proceed by minimizing a proximity function can be used to obtain optimal approximate solutions to the problem. We present an extension of the proximity function approach that generalizes the linear split feasibility problem to allow for non-linear mappings. Our algorithm is based on the principle of majorization–minimization, is amenable to quasi-Newton acceleration, and comes complete with convergence guarantees under mild assumptions. Furthermore, we show that the Euclidean norm appearing in the proximity function of the non-linear split feasibility problem can be replaced by arbitrary Bregman divergences. We explore several examples illustrating the merits of non-linear formulations over the linear case, with a focus on optimization for intensity-modulated radiation therapy.
10 citations