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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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10 Dec 2009
TL;DR: A brief historical overview of linear programming can be found in this article, with a brief history and a brief overview of the main techniques involved in the development of linear programs. But the main focus of this paper is on the transformation of variables.
Abstract: Linear Equations, Inequalities, Linear Programming: A Brief Historical Overview.- Formulation Techniques Involving Transformations of Variables.- Intelligent Modeling Essential to Get Good Results.- Polyhedral Geometry.- Duality Theory and Optimality Conditions for LPs.- Revised Simplex Variants of the Primal and Dual Simplex Methods and Sensitivity Analysis.- Interior Point Methods for LP.- Sphere Methods for LP.- Quadratic Programming Models.

32 citations

01 Jan 1991
TL;DR: In this paper, a detailed study on rigid body impact laws and the assumption of contact compliance is investigated, and a systematic method for the analysis and simulation of such systems is proposed.
Abstract: In many engineering applications such as assembly of mechanical components, robot manipulation, gripping, fixturing and part feeding, there are situations in which a rigid body is subject to multiple frictional contacts with other bodies. It is proposed to develop a systematic method for the analysis and simulation of such systems. A detailed study is presented on rigid body impact laws, and the assumption of contact compliance is investigated. Comments University of Pennsylvania Department of Computer and Information Sciences Technical Report No. MSCIS-91-48. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/320 Figure 3.3: Cases of collision The final velocities can be obtained as following:

32 citations

Journal ArticleDOI
TL;DR: In this article, the problem of grasping work pieces with frictional multifingered grippers is formulated in a compact form as a nonsymmetric linear complementary problem (LCP). Necessary and sufficient conditions which guarantee the solvability of the problem are derived.
Abstract: This paper deals with the problem of grasping work pieces with frictional multifingered grippers. The two types of frictional fingers „hard finger” and „soft finger” are treated. Hard fingers have the ability to constraint the object displacements on the normal and tangential directions to the object boundary, whereas soft fingers have in addition the ability to constraint the rotation of the object about the normal axis through the point of contact. The unilateral contact problem and the frictional problem are formulated in a compact form as a nonsymmetric Linear Complementarity Problem (LCP). Necessary and sufficient conditions which guarantee the solvability of the problem are derived. Also numerical examples computing the normal and tangential reactions, the slip Lagrange multiplier and the rigid body displacements and rotations are given. Die vorliegende Arbeit beschaftigt sich mit dem Problems, Werkstucke mit einem vielfingerigen Reibungsgreifer aufzugreifen. Dabei werden zwei Typen von Reibungsfingern behandelt, „harte” und „sanfte” Finger. Harte Finger haben die Fahigkeit, die Verschiebungen des Objectes auf normale und tangentiale Richtungen bezogen auf die Objektoberflache zu beschranken, wahrend die sanften Finger zusatzlich die Fahigkeit haben, die Drehung des Objectes auf die Rotation um die Normalachse durch den Kontaktpunkt einzuschranken. Sowohl das einseitige Kontaktproblem als auch das Reibungsproblem werden in kompakter Form als unsymmetrisches lineares Komplementaritatsproblem formuliert. Notwendige und hinreichende Bedingungen, die die Losbarkeit des Problems sichern, werden abgeleitet. Ebenso werden numerische Beispiele angegeben, in denen die Normal- und Tangentialreaktion, die Lagrangeschen Gleitmultiplikatoren und die Verschiebungen und Rotationen des Festkorpers berechnet werden.

31 citations

Journal ArticleDOI
TL;DR: The nonsmooth discrete element method (NDEM) has the potential of high computational efficiency for rapid exploration of large design space of systems for processing and transportation of mineral o....

31 citations


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

  • ...This includes solving a MLCP similar to Eq....

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  • ...Stepping the system position and velocity, (xi, vi) → (xi + 1, vi + 1), from time ti to ti + 1= ti+Δt involve solving amixed linear complementarity problem (MLCP) [13] of the form Hzþ b ¼ wl−wu 0 ≤ z−l⊥wl ≥ 0 0 ≤ u−z⊥wu ≥ 0 ð5Þ where H ¼ M ‐GTn ‐...

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  • ...Stepping the system position and velocity, (xi, vi) → (xi + 1, vi + 1), from time ti to ti + 1= ti+Δt involve solving amixed linear complementarity problem (MLCP) [13] of the form...

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  • ...[2] and summarized in Appendix A, for solving the MLCP (5)....

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Book ChapterDOI
01 Jan 1994
TL;DR: The most important existence and complexity results of the LCP are reviewed and direct, iterative and enumerative algorithms are discussed together with their benefits and drawbacks.
Abstract: This paper presents a survey of the Linear Complementarity Problem (LCP). The most important existence and complexity results of the LCP are first reviewed. Direct, iterative and enumerative algorithms are then discussed together with their benefits and drawbacks.

31 citations