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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 article presents computationally efficient algorithms for modeling two special cases of rigid contact---contact with only viscous friction and contact without slip---that have particularly useful applications in robotic locomotion and grasping.
Abstract: This article presents computationally efficient algorithms for modeling two special cases of rigid contact---contact with only viscous friction and contact without slip---that have particularly useful applications in robotic locomotion and grasping. Modeling rigid contact with Coulomb friction generally exhibits $O(n^3)$ expected time complexity in the number of contact points and $2^{O(n)}$ worst-case complexity. The special cases we consider exhibit $O(m^3 + m^2n)$ time complexity ($m$ is the number of independent coordinates in the multi rigid body system) in the expected case and polynomial complexity in the worst case; thus, asymptotic complexity is no longer driven by number of contact points (which is conceivably limitless) but instead is more dependent on the number of bodies in the system (which is often fixed). These special cases also require considerably fewer constrained nonlinear optimization variables thus yielding substantial improvements in running time. Finally, these special cases also afford one other advantage: the nonlinear optimization problems are numerically easier to solve.
2 citations
Cites background or methods from "Linear complementarity, linear and ..."
...4) Algorithm: We use the theorem above to make a minor modification to the Principal Pivot Method I [5, 15] (PPM), which solves LCPs with P -matrices (complex square matrices with fully non-negative principal minors [15] that includes positive semi-definite matrices as a proper subset)....
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...Algorithm [15]) to worst-case polynomial in the number of contact points; () significant reduction in the number of nonlinear optimization problem variables; and () a positivesemi-definite-matrix linear complementarity problem (LCP), in place of a copositive-plus LCP, which is demonstrably easier to solve [8] (i....
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...Lemke’s Algorithm can exhibit exponential complexity [15], though polynomial time is expected....
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01 Jan 2003
TL;DR: A future direction that is based on an evolutionary analysis about the behaviors of negotiation to model the multi-agent system is proposed.
Abstract: Game theory models and analyzes the situations of conflict and cooperation among independent decision-makers. We can view the runs of a multi-agent system as a game where the interactions of agents is referred as the strategies of players, thenceforth we can use game theory to model the knowledge of agents. This paper review the basic results of game theory and propose a future direction that is based on an evolutionary analysis about the behaviors of negotiation to model the multi-agent system.
2 citations
Cites background from "Linear complementarity, linear and ..."
...He will consider if it is not worth-while for him to dislocate the current coalition structure and to form a new coalition around him which would be more interesting for him in terms of payoff....
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TL;DR: In this paper, the authors apply the concept of (0, k)-epi to the study of solvability of complementarity problems, and some interesting relations are established between the complementarity theory and the nonlinear analysis.
2 citations
01 Jan 2010
TL;DR: In this article, the authors discuss some factors that may have led to this state of affairs and elaborate an argument for the repeatedly made assertion that Markowitz's critical line algorithm and Philip Wolfe's simplex method for quadratic programming are equivalent.
Abstract: Despite his fame as the father of modern portfolio selection theory, Harry Markowitz’s pioneering efforts in the methodology of quadratic programming are surprisingly obscure. This article is primarily about Markowitz’s critical line algorithm as a contribution to the early history of quadratic programming (as distinct from the more specialized portfolio selection problem). After documenting our claim that the critical line algorithm received scant attention around the time of its introduction, we discuss some factors that may have led to this state of affairs. We then elaborate an argument for the repeatedly made assertion that Markowitz’s critical line algorithm and Philip Wolfe’s simplex method for quadratic programming are equivalent. We do this by relating both of them to the parametric principal pivoting method of quadratic programming and linear complementarity theory.
2 citations
24 Apr 2000
TL;DR: The paper gives a general description of friction and a walking machine example and influences the power budget and the selection of motors, and it influences significantly the control concepts.
Abstract: In realizing walking machines friction plays an important role which cannot be neglected. Friction will be generated in contacts of the feet with the ground and in drives including gears. Friction influences the power budget and thus the selection of motors, and it influences significantly the control concepts. The paper gives a general description of friction and a walking machine example.
2 citations