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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 direct sparse orthogonalization methodology based on Givens rotations and a static sparsity data structure is proposed for both phases, with a Linpack-like downdating without resorting to hyperbolic rotations.
Abstract: A finite continuation method for solving linear programs (LPs) has been recently put forward by K. Madsen and H. B. Nielsen which, to improve its performance, can be thought of as a Phase-I for a non-simplex active-set method (also known as basis-deficiency-allowing simplex variation); this avoids having to start the simplex method from a highly degenerate square basis. An efficient sparse implementation of this combined hybrid approach to solve LPs requires the use of the same sparse data structure in both phases, and a way to proceed in Phase-II when a non-square working matrix is obtained after Phase-I. In this paper a direct sparse orthogonalization methodology based on Givens rotations and a static sparsity data structure is proposed for both phases, with a LINPACK-like downdating without resorting to hyperbolic rotations. Its sparse implementation (recently put forward by us) is of reduced-gradient type, regularization is not used in Phase-II, and occasional refactorizations can take advantage of row orderings and parallelizability issues to decrease the computational effort.
07 Aug 2002
TL;DR: A force and attitude control law is proposed of an asteroid sample return robot to obtain an enough constraint force for taking samples from the surface of the asteroid during contact to pay attention to the complementarity.
Abstract: In this paper, we propose a force and attitude control law of an asteroid sample return robot to obtain an enough constraint force for taking samples from the surface of the asteroid during contact. In a phenomenon of the impact between the robot and the asteroid, there is a complementary relation between the robot acceleration and the constraint force on the contact point. To pay attention to the complementarity, we derive a condition to constrain the robot on the surface of the asteroid based on complementarity system (CS). We design a control law which achieves the desired force and attitude with keeping the contact, and verify the effectiveness of the proposed control law by experiments.
01 Jan 2010
TL;DR: In this article, a method for the two-person zero-sum and non-zero-sum games that the payoffs are represented by fuzzy data, has been investigated, based on Linear Complementarity Problem (LCP) which unifies bimatrix games.
Abstract: The conventional game theory is based on known payoffs. In the real situations, usually the payoffs are not known and have to be approximated. In this paper, a method for the two-person zero-sum and non-zero-sum games that the payoffs are represented by fuzzy data, has been investigated. The procedure is based on Linear Complementarity Problem (LCP) which unifies bimatrix games.
25 Apr 2011
TL;DR: In this paper, a feasible interior point method is proposed for solving the NP-hard absolute value equation (AVE) when the singular values of A exceed one, and the solution to AVE is existent and unique under suitable assumptions.
Abstract: A feasible interior point method is proposed for solving the NP-hard absolute value equation (AVE) when the singular values of A exceed one. We formulate the NP-hard AVE as linear complementary problem, and prove that the solution to AVE is existent and unique under suitable assumptions. Then we present a feasible interior point algorithm for AVE based on the Newton direction and centering direction. We show that this algorithm has the polynomial complexity. Preliminary numerical results show that this method is promising.
Cites background or methods from "Linear complementarity, linear and ..."
...It is well known that the standard linear complementarity problem has been studied well in the literature [3,4,15,16]....
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...[15] is a good reference for pivoting methods developed to solve LCP....
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