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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 2010
TL;DR: The semidefinite linear complementarity problem (SDLCP) as discussed by the authors is ageneralization of the LCP, in which linear transformations replace matrices and the cone of positive semidefinite matrices replaces the nonnegative orthant.
Abstract: The semidefinite linear complementarity problem (SDLCP) is ageneralization of the linear complementarity problem (LCP) inwhich linear transformations replace matrices and the cone ofpositive semidefinite matrices replaces the nonnegative orthant.We study a number of linear transformation classes (some of whichare introduced for the first time) and extend several knownresults in LCP theory to the SDLCPs, and in particular, resultswhich are related to the key properties of uniqueness, feasibilityand convexity. Finally, we introduce some new characterizationsrelated to the class of matrices E* and the uniqueness ofthe LCPs.
2 citations
Cites background from "Linear complementarity, linear and ..."
...Extensive coverage of linear complementarity problem theory is available in the monographs (Cottle et al., 1992; Murty, 1988) and the research articles in their reference lists....
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TL;DR: It is shown that the 2-LCP is strongly NP-hard, and it can be solved in polynomial time if it is sign-balanced, i.e., each row of the matrix has at most one positive and one negative entry.
Abstract: In this paper, we consider the sparse linear complementarity problem, denoted by k-LCP: the coefficient matrices are restricted to have at most k nonzero entries per row. It is known that the 1-LCP is solvable in linear time, and the 3-LCP is strongly NP-hard. We show that the 2-LCP is strongly NP-hard, and it can be solved in polynomial time if it is sign-balanced, i.e., each row of the matrix has at most one positive and one negative entry. Our second result matches the currently best-known complexity bound for the corresponding sparse linear feasibility problem. In addition, we show that an integer variant of the sign-balanced 2-LCP is weakly NP-hard and pseudo-polynomially solvable, and the generalized 1-LCP is strongly NP-hard.
2 citations
Posted Content•
TL;DR: The main goal of this paper is the construction of a simple explicit reduction of any LCP(q,M) that can be verified as belonging to PPAD via the graph induced by the generic Lemke algorithm with some positive covering vector d, to a symmetric 2-NASH.
Abstract: The linear complementarity problem, LCP(q,M), is defined as follows. For given M,q find z such that q+Mz>=0, z>=0, z(q + M z)=0,or certify that there is no such z. It is well known that the problem of finding a Nash equilibrium for a bimatrix game (2-NASH) can be formulated as a linear complementarity problem (LCP). In addition, 2-NASH is known to be complete in the complexity class PPAD (Polynomial-time Parity Argument Directed). However, the ingeniously constructed reduction (which is designed for any PPAD problem) is very complicated, so while of great theoretical significance, it is not practical for actually solving an LCP via 2-NASH, and it may not provide the potential insight that can be gained from studying the game obtained from a problem formulated as an LCP (e.g. market equilibrium). The main goal of this paper is the construction of a simple explicit reduction of any LCP(q,M) that can be verified as belonging to PPAD via the graph induced by the generic Lemke algorithm with some positive covering vector d, to a symmetric 2-NASH. In particular, any endpoint of this graph (with the exception of the initial point of the algorithm) corresponds to either a solution or to a so-called secondary ray. Thus, an LCP problem is verified as belonging to PPAD if any secondary ray can be used to construct, in polynomial time, a certificate that there is no solution to the problem. We achieve our goal by showing that for any M,q and a positive d satisfying a certain nondegeneracy assumption with respect to M, we can simply and directly construct a symmetric 2-NASH whose Nash equilibria correspond one-to-one to the end points of the graph induced by LCP(q,M) and the Lemke algorithm with a covering vector d. We note that for a given M the reduction works for all positive d with the exception of a subset of measure 0.
2 citations
01 Jan 2009
TL;DR: A survey of recent literature on deregulated (aka restructured) electricity markets is presented in this paper, where the most important research areas related to the energy market are classified based on 28 critical research areas such as auction based pricing, bidding strategy formula, market equilibria and market power.
Abstract: Availability of a large volume of recent literature on deregulated (aka restructured) electricity markets 22 underscores the importance of the research needs to ensure proper design and functioning of the mar23 kets Researchers have made significant contributions fueling the evolution of the fundamental market 24 design changes that have taken place since the beginning of the restructuring process Due to the vast 25 scope, existing survey papers are focused on particular facets of deregulated electricity markets We 26 adopt a similar approach by focusing on the most important research areas related to the energy market 27 The contributions of the survey paper lie in the novel approach used in classifying the literature based on 28 critical research areas Some areas of research such as auction based pricing, bidding strategy formula29 tion, market equilibria, and market power are reviewed in a different light than other existing survey 30 papers We conclude by providing some future research directions for the energy markets 31
2 citations
Posted Content•
TL;DR: A control architecture enabling to drive virtual humans in a real-time immersed way, and to interact with the product, through motion capture is drawn, but it is shown this control scheme can lead to unfeasible movements because of the lack of balance control.
Abstract: The work presented here is aimed at introducing a virtual human controller in a virtual prototyping framework After a brief introduction describing the problem solved in the paper, we describe the interest as for digital humans in the context of concurrent engineering This leads us to draw a control architecture enabling to drive virtual humans in a real-time immersed way, and to interact with the product, through motion capture Unfortunately, we show this control scheme can lead to unfeasible movements because of the lack of balance control Introducing such a controller is a problem that was never addressed in the context of real-time We propose an implementation of a balance controller, that we insert into the previously described control scheme Next section is dedicated to show the results we obtained Finally, we propose a virtual reality platform into which the digital character controller is integrated
2 citations