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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.
Citations
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TL;DR: In this article, the complexity of deciding whether a given point is a critical point and whether a polynomial has a point of that type is studied. But the complexity is not bounded.
3 citations
04 Jun 2019
TL;DR: The analysis of infeasible subproblems, which is an important component of most major MIP solvers, has been hardly studied in the context of MINLPs.
Abstract: Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer programming (MIP) solvers in the sense that they are based on a branch-and-cut algorithm, enhanced by various heuristics, domain propagation, and presolving techniques. However, the analysis of infeasible subproblems, which is an important component of most major MIP solvers, has been hardly studied in the context of MINLPs. There are two main approaches for infeasibility analysis in MIP solvers: conflict graph analysis, which originates from artificial intelligence and constraint programming, and dual ray analysis.
3 citations
01 Jan 2017
TL;DR: In this article, a preliminary numerical study aimed to improve the safety on haul roads in surface mining is presented, where the interaction and collision between granular berms and ultra-class haul trucks are investigated.
Abstract: The paper presents a preliminary numerical study aimed to improve the safety on haul roads in surface mining. The interaction and collision between granular berms and ultra-class haul trucks are in ...
3 citations
Cites background from "Linear complementarity, linear and ..."
...Stepping the system position and velocity, (xi,vi) → (xi+1,vi+1), from time ti to ti+1 = ti + h involves solving a mixed complementarity problem [13]....
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TL;DR: This paper considers the design of constrained linear phase finite impulse response (FIR) filters as a linear complementarity problem (LCP), which is solved using Lemke's algorithm, a refined mathematical formalism with useful theoretical results.
Abstract: In this paper, the design of constrained linear phase finite impulse response (FIR) filters is considered. The problem is formulated as a linear complementarity problem (LCP), which is solved using Lemke's algorithm. The LCP is a refined mathematical formalism with useful theoretical results. The digital filters presented meet efficiently the specifications of the magnitude response error. The used algorithm is a direct one and therefore, there is no need for matrix inversion. However, in the iterative methods that are frequently used, the bulk of the design computation is concerned with the evaluation of matrix inversion in order to solve a system of equations. Examples to illustrate the proposed method are presented. Copyright © 2005 John Wiley & Sons, Ltd.
3 citations
01 Jan 1998
TL;DR: More general optimization problems which are not always based on physical considerations arise in several engineering problems, for instance problems of optimal design of structures, control, identification and reliability analysis of structures and mechanical systems.
Abstract: The problem of finding an extremum of a given function over the space where the function is defined or over a subset of it, is called an optimization problem. In mechanics several “principles” which govern physical phenomena in general and the response of mechanical systems in particular are written in the form of an optimization problem. The principles of minimum potential energy in statics, the maximum dissipation principle in dissipative media and the least action principle in dynamics are some examples (see, among others, Hamel, 1949, Lippmann, 1972, Cohn and Maier, 1979, de Freitas, 1984, de Freitas and Smith, 1985, Panagiotopoulos, 1985, Hartmann, 1985, Sewell, 1987, Bazant and Cedolin, 1991). More general optimization problems which are not always based on physical considerations arise in several engineering problems, for instance problems of optimal design of structures, control, identification and reliability analysis of structures and mechanical systems.
3 citations