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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 presents an application of a linear complementarity problem where M is a P-matrix but, in general, is neither an H-Matrix nor a positive definite matrix, and extends the idea such that the calculations can be done by a computer with rigorous error control.
Abstract: In this paper, we present an application of a linear complementarity problem where M is a P-matrix but, in general, is neither an H-matrix nor a positive definite matrix. This application occurs originally in [J. Rohn, Linear Algebra Appl., 126 (1989), pp. 39--78], which is less known to the LCP community. Its focus is in computing the exact interval enclosures of the components of the solution set of an interval linear system. We extend the idea such that the calculations can be done by a computer with rigorous error control.
62 citations
TL;DR: In this article, a percussion drilling machine is examined as an example for mechanical systems with unilateral contacts, and the constrained motion of the system and simultaneously the constraint forces are taken into account by algebraic relations.
Abstract: In the following a percussion drilling machine is examined as an example for mechanical systems with unilateral contacts. It is characteristic for such systems that the number of degrees of freedom changes during motion. To avoid a description of each possible system state using different sets of minimal coordinates, the constrained motion is taken into account by algebraic relations. This method has the advantage that the motion of the system and simultaneously the constraint forces are available, which is necessary to obtain conditions for a change in the state of the system. Furthermore different combinations of constraints can be easily taken into consideration in this way.
62 citations
Additional excerpts
...With this property it is obvious that even ( ΛNC ΛTC )T ( εN 0 0 0 )( ġNC ġTC ) ≤ 0 (109)...
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TL;DR: A problem in visual labeling and artificial neural networks, equivalent to finding Nash equilibria for polymatrix n-person games, may be solved by the copositive-plus Lemke algorithm.
61 citations
TL;DR: In this paper, the global uniqueness and solvability properties of tensor complementarity problems (TCPs) for some special structured tensors are studied. And the modulus equation for TCPs is also studied.
Abstract: In this paper, we study the global uniqueness and solvability (GUS-property) of tensor complementarity problems (TCPs) for some special structured tensors. The modulus equation for TCPs is also pro...
61 citations
Cites background from "Linear complementarity, linear and ..."
...It is well known that the LCP(q,A) is equivalent to the following modulus equation (see [17,18]):...
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TL;DR: A potential reduction algorithm is applied to solve the general linear complementarity problem GLCP and it is shown that the algorithm is a fully polynomial-time approximation scheme FPTAS for computing an e-approximate stationary point of the G LCP.
Abstract: We apply a potential reduction algorithm to solve the general linear complementarity problem GLCP
minimizeâxTy
subject toâAx + By + Cz = qâandâx, y, z ⥠0.
We show that the algorithm is a fully polynomial-time approximation scheme FPTAS for computing an e-approximate stationary point of the GLCP. Note that there are some GLCPs in which every stationary point is a solution xTy = 0. These include the LCPs with row sufficient matrices. We also show that the algorithm is a polynomial-time algorithm for a special class of GLCPs.
61 citations
Cites background from "Linear complementarity, linear and ..."
...In fact, Murty [11] has shown that Lemke's algorithm converges in an exponential number of steps for an instance of the standard (convex) linear complementarity problem....
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