scispace - formally typeset
Search or ask a question
Book

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.
Citations
More filters
Book ChapterDOI
17 Jan 2017
TL;DR: The criss-cross method is able to compute solution of a linear complementarity problem in finite steps in case of some new matrix classes and a numerical illustration is presented to show a comparison between criss -cross method and Lemke's algorithm with respect to number of iterations before finding a solution.
Abstract: In this paper we consider criss-cross method for finding solution of a linear complementarity problem. The criss-cross method is a pivoting procedure. We show that the criss-cross method is able to compute solution of a linear complementarity problem in finite steps in case of some new matrix classes. We present a numerical illustration to show a comparison between criss-cross method and Lemke’s algorithm with respect to number of iterations before finding a solution. Finally we raise an open problem in the context of criss-cross method.

28 citations

Journal ArticleDOI
TL;DR: A modulus-based nonsmooth Newton's method is established and its locally quadratical convergence conditions are presented and it is shown that the proposed methods are efficient and accelerate the convergence performance of the moduli-based matrix splitting iteration methods.

28 citations


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

  • ..., the linear and quadratic programming, the economies with institutional restrictions upon prices, the optimal stopping in Markov chain, and the free boundary problems; see [1,2] for details....

    [...]

  • ...It is known from [2] that the linear complementarity problem LCP(M, q) is completely equivalent to solving the nonlinear equation F(x) = 0, (3) where F is a function from Rn into itself defined by F(x) := (M + I)x + (M − I)|x| + q....

    [...]

  • ...By equivalently reformulating (3) as an implicit fixed-point equation, Murty presented a modulus iteration method in [2], which was defined as the solution of a system of linear equations at each iteration....

    [...]

Journal ArticleDOI
TL;DR: A generalized Accelerated Overrelaxation (GAOR) method is used and the convergence of this method for solving linear complementarity problems is analyzed and improved on the convergence region with acknowledgement of the maximum norm.
Abstract: In this paper, we use a generalized Accelerated Overrelaxation (GAOR) method and analyze the convergence of this method for solving linear complementarity problems. Furthermore, we improve on the convergence region of this method with acknowledgement of the maximum norm. A numerical example is also given, to illustrate the efficiency of our results.

28 citations


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

  • ...The Linear Complementarity Problem (LCP) is one of the fundamental problems in optimization and mathematical programming [1]....

    [...]

  • ...For more details, see [1, 2] and the references therein....

    [...]

Journal ArticleDOI
TL;DR: The proposed iterative method is simple and easy to construct, and requiring only third Fréchet differentiation, and a comparison between the efficiency of the proposed method and existing ones is made.
Abstract: In this paper, we present an (m+1)-step iterative method of convergence order (m+2) for solving linear complementarity problems. The proposed iterative method is simple and easy to construct, and requiring only third Frechet differentiation. Computational efficiency in its general form is discussed and a comparison between the efficiency of the proposed method and existing ones is made. The performance is tested through numerical experiments on some test problems.

28 citations

Proceedings ArticleDOI
26 May 2015
TL;DR: In this paper, a novel aerial manipulation system is proposed, in which the mechanical structure of the system, the number of thrusters and their geometry are derived from technical optimization problems.
Abstract: In this paper a novel aerial manipulation system is proposed. The mechanical structure of the system, the number of thrusters and their geometry will be derived from technical optimization problems. The aforementioned problems are defined by taking into consideration the desired actuation forces and torques applied to the end-effector of the system. The framework of the proposed system is designed in a CAD Package in order to evaluate the system parameter values. Following this, the kinematic and dynamic models are developed and an adaptive backstepping controller is designed aiming to control the exact position and orientation of the end-effector in the Cartesian space. Finally, the performance of the system is demonstrated through a simulation study, where a manipulation task scenario is investigated.

28 citations