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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 paper considers EPCCs with convex quadratic objective functions and one set of complementarity constraints and proposes a possible generalization of the homotopy method for finding stationary points of MPCCs.
Abstract: In the paper we consider EPCCs with convex quadratic objective functions and one set of complementarity constraints. For this class of problems we propose a possible generalization of the homotopy method for finding stationary points of MPCCs. We analyze the difficulties which arise from this generalization. Numerical results illustrate the performance for randomly generated test problems.
1 citations
Cites background from "Linear complementarity, linear and ..."
...(2) We assume that b > 0, which is sufficient for the linear complementarity problem (2) to be uniquely solvable, [4]....
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1 citations
10 Dec 2003
TL;DR: The paper deals with the problem to optimize the path of a robot arm being mounted on a mobile platform, which is constrained to the environment by unilateral constraints, and a compact spatial formulation of Signorini's law is used.
Abstract: The paper deals with the problem to optimize the path of a robot arm being mounted on a mobile platform, which is constrained to the environment by unilateral constraints. The goal is to minimize the needed time as well as the energy consumption under the boundary condition to avoid a change in the state of contact at the unilateral constraints. The contact behaviour of the system is described with a linear complementarity problem LCP. For its solution a compact spatial formulation of Signorini's law is used. The temporal courses of the joint angle velocities are described by ramp functions. The ramp parameters are used as the optimization parameters. Therewith it is possible to vary the different phases of acceleration and constant movement for each joint separately, enabling the optimization algorithm to find an optimal temporal course for the robot's kinematic quantities.
1 citations
TL;DR: The comparison results showed that preconditioned SSOR methods accelerate the convergent rate of the original SSOR method.
Abstract: In this paper, we consider the preconditioned iterative methods for solving linear complementarity problem associated with an M matrix. Based on the generalized Gunawardena’s preconditioner, two preconditioned SSOR methods for solving the linear complementarity problem are proposed. The convergence of the proposed methods are analyzed, and the comparison results are derived. The comparison results showed that preconditioned SSOR methods accelerate the convergent rate of the original SSOR method. Numerical examples are used to illustrate the theoretical results.
1 citations
TL;DR: This paper generalizes concepts like the value and equilibrium of a bimatrix game to the general linear transformations defined on a finite dimensional space and proves some known classical results in the theory of linear complementarity problems for this type of Z -transformations.
Abstract: In this paper, we define bi-linear games as a generalization of the bimatrix games In particular, we generalize concepts like the value and equilibrium of a bimatrix game to the general linear transformations defined on a finite dimensional space For a special type of Z-transformation we observe relationship between the values of the linear and bi-linear games Using this relationship, we prove some known classical results in the theory of linear complementarity problems for this type of Z-transformations
1 citations