Florian A. Potra In this paper we present novel data-driven optimization models for Support Vector Machines (SVM), with the aim of linearly separating two sets of points that have non-disjoint convex closures. Traditional classi cation algorithms assume that the training data points are always known exactly. However, real-life data are often subject to noise. To handle such uncertainty, we … Read more
In this paper we consider a transportation problem under uncertainty related to gypsum replenishment for a cement producer. The problem is to determine the number of vehicles to book at the beginning of each week to replenish gypsum at all the cement factories of the producer in order to minimize the total cost, given by … Read more
This paper presents some fundamental results about sufficient linear weighted complementarity problems. Such a problem depends on a nonnegative weight vector. If the weight vector is zero, the problem reduces to a sufficient linear complementarity problem that has been extensively studied. The introduction of the more general notion of a weighted complementarity problem (wCP) was … Read more
Three interior point methods are proposed for sufficient horizontal linear complementarity problems (HLCP): a large update path following algorithm, a first order corrector-predictor method, and a second order corrector-predictor method. All algorithms produce sequences of iterates in the wide neighborhood of the central path introduced by Ai and Zhang. The algorithms do not depend on … Read more
This paper introduces the notion of a weighted Complementarity Problem (wCP), which consists in finding a pair of vectors $(x,s)$ belonging to the intersection of a manifold with a cone, such that their product in a certain algebra, $x\circ s$, equals a given weight vector $w$. When $w$ is the zero vector, then wCP reduces … Read more
The present work aims at comparing the performance of several quadratic programming (QP) solvers for simulating large-scale frictional rigid-body systems. Traditional time-stepping schemes for simulation of multibody systems are formulated as linear complementarity problems (LCPs) with copositive matrices. Such LCPs are generally solved by means of Lemketype algorithms and solvers such as the PATH solver … Read more
A new class of infeasible interior point methods for solving sufficient linear complementarity problems requiring one matrix factorization and $m$ backsolves at each iteration is proposed and analyzed. The algorithms from this class use a large $(\caln_\infty^-$) neighborhood of an infeasible central path associated with the complementarity problem and an initial positive, but not necessarily … Read more
We consider the problem of finding an $\epsilon-$optimal solution of a standard linear program with real data, i.e., of finding a feasible point at which the objective function value differs by at most $\epsilon$ from the optimal value. In the worst-case scenario the best complexity result to date guarantees that such a point is obtained … Read more
In this work we present a framework for the convergence analysis in a measure differential inclusion sense of a class of time-stepping schemes for multibody dynamics with contacts, joints, and friction. This class of methods solves one linear complementarity problem per step and contains the semi-implicit Euler method, as well as trapezoidallike methods for which … Read more
A first order affine scaling method and two $m$th order affine scaling methods for solving monotone linear complementarity problems (LCP) are presented. All three methods produce iterates in a wide neighborhood of the central path. The first order method has $O(nL^2(\log nL^2)(\log\log nL^2))$ iteration complexity. If the LCP admits a strict complementary solution then both … Read more