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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: The history of the International Symposia on Mathematical Programming from the 0th in 1949 to the 19th in 2006 is recounted.
Abstract: This article briefly recounts the history of the International Symposia on Mathematical Programming from the 0th in 1949 to the 19th in 2006. Included in the summary are the dates, locations, organizers, sponsors, award winners, and special characteristics of each Symposium.
7 citations
07 Dec 2014
TL;DR: This work considers a real-valued function that can only be evaluated with error, and introduces a sequential Bayesian procedure that approximate the probability that the function is convex based on the posterior using Monte Carlo simulation.
Abstract: Consider a real-valued function that can only be evaluated with error. Given estimates of the function values from simulation on a finite set of points, we seek a procedure to detect convexity or non-convexity of the true function restricted to those points. We review an existing frequentist hypothesis test, and introduce a sequential Bayesian procedure. Our Bayesian procedure applies for both independent sampling and sampling with common random numbers, with known or unknown sampling variance. In each iteration, we collect a set of samples and update a posterior distribution on the function values, and use that as the prior belief in our next iteration. We then approximate the probability that the function is convex based on the posterior using Monte Carlo simulation.
7 citations
TL;DR: In this paper, a new type of numerical method for the calculation of force distribution on multifingered frictional grippers is given, where the two types of contact, "hard" and "soft" finger, are considered.
7 citations
TL;DR: In this article, the authors compare the numerical performance of several methods for solving the discrete contact problem arising from the finite element discretisation of elastic systems with numerous contact points, formulated as a variational inequality and discretised using piecewise quadratic finite elements on a triangulation of the domain.
Abstract: We compare the numerical performance of several methods for solving the discrete contact problem arising from the finite element discretisation of elastic systems with numerous contact points. The problem is formulated as a variational inequality and discretised using piecewise quadratic finite elements on a triangulation of the domain. At the discrete level, the variational inequality is reformulated as a classical linear complementarity system. We compare several state-of-art algorithms that have been advocated for such problems. Computational tests illustrate the use of these methods for a large collection of elastic bodies, such as a simplified bidimensional wall made of bricks or stone blocks, deformed under volume and surface forces.
7 citations
TL;DR: This paper shows that it can be used to use a rank one update technique in the adaptive algorithm so that the number of overall arithmetic operations is theoretically bounded by O(n3L).
Abstract: In this paper we propose an O(n3L) algorithm which is a modification of the path following algorithm [8] for a linear complementarity problem. The path following algorithm has to take a short step size in each iteration in order to bound the number of overall arithmetic operations by O(n3L). In practical computation, we can determine the step size adaptively. Mizuno, Yoshise, and Kikuchi [11] reported that such an adaptive algorithm required about O(L) iterations for some test problems. Here we show that we can use a rank one update technique in the adaptive algorithm so that the number of overall arithmetic operations is theoretically bounded by O(n3L).
7 citations