Impulsive Optimal Control of Hybrid Finite-Dimensional Lagrangian Systems

The scope of this dissertation addresses numerical and theoretical issues in the impulsive control of hybrid finite-dimensional Lagrangian systems. In order to treat these aspects, a modeling framework is presented based on the measure-differential inclusion representation of the Lagrangian dynamics. The main advantage of this representation is that it enables the incorporation of set-valued force … Read more

Necessary Conditions for the Impulsive Optimal Control of Multibody Mechanical Systems

In this work, necessary conditions for the impulsive optimal control of multibody mechanical systems are stated. The conditions are obtained by the application subdifferential calculus techniques to extended-valued lower semi-continuous generalized Bolza functional that is evaluated on multiple intervals. Contrary to the approach in literature so far, the instant of possibly impulsive transition is considered … Read more

Projections Onto Super-Half-Spaces for Monotone Variational Inequality Problems in Finite-Dimensional Spaces

The variational inequality problem (VIP) is considered here. We present a general algorithmic scheme which employs projections onto hyperplanes that separate balls from the feasible set of the VIP instead of projections onto the feasible set itself. Our algorithmic scheme includes the classical projection method and Fukushima’s subgradient projection method as special cases. Citation Technical … Read more

An LPCC Approach to Nonconvex Quadratic Programs

Filling a gap in nonconvex quadratic programming, this paper shows that the global resolution of a feasible quadratic program (QP), which is not known a priori to be bounded or unbounded below, can be accomplished in finite time by solving a linear program with linear complementarity constraints, i.e., an LPCC. Alternatively, this task can be … Read more

Large-Scale Parallel Multibody Dynamics with Frictional Contact on the Graphical Processing Unit

In the context of simulating the frictional contact dynamics of large systems of rigid bodies, this paper reviews a novel method for solving large cone complementarity problems by means of a fixed-point iteration algorithm. The method is an extension of the Gauss-Seidel and Gauss-Jacobimethods with overrelaxation for symmetric convex linear complementarity problems. Convergent under fairly … Read more

On a class of superlinearly convergent polynomial time interior point methods for sufficient LCP

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

A Two Stage Stochastic Equilibrium Model for Electricity Markets with Two Way Contracts

This paper investigates generators’ strategic behaviors in contract signing in the forward market and power transaction in the electricity spot market. A stochastic equilibrium program with equilibrium constraints (SEPEC) model is proposed to characterize the interaction of generators’ competition in the two markets. The model is an extension of a similar model proposed by Gans, … Read more

Fischer-Burmeister Complementarity Function on Euclidean Jordan Algebras

Recently, Gowda et al. [10] established the Fischer-Burmeister (FB) complementarity function (C-function) on Euclidean Jordan algebras. In this paper, we prove that FB C-function as well as the derivatives of the squared norm of FB C-function are Lipschitz continuous. Citation Research Report CORR 2007-17, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, … Read more

An iterative approach for cone complementarity problems for nonsmooth multibody dynamics

Aiming at a fast and robust simulation of large multibody systems with contacts and friction, this work presents a novel method for solving large cone complementarity problems by means of a fixed-point iteration. The method is an extension of the Gauss-Seidel and Gauss-Jacobi method with overrelaxation for symmetric convex linear complementarity problems. The method is … Read more

An Algorithm for the Fast Solution of Linear Complementarity Problems

This paper studies algorithms for the solution of mixed symmetric linear complementarity problems. The goal is to compute fast and approximate solutions of medium to large sized problems, such as those arising in computer game simulations and American option pricing. The paper proposes an improvement of a method described by Kocvara and Zowe that combines … Read more