Homogenization of Mixed Horizontal LCPs and Applications

Abstract

In optimization, a homogeneous model is an artificial transformation of a given problem. The transformation is done such that the homogeneous problem has always a solution even if the original problem does not. Moreover, without having any assumption on the feasibility of the original problem, the homogeneous model is able to provide the solution if it exists, or a certificate of infeasibility otherwise. The first part of the thesis will introduce a homogeneous model for mixed linear complementarity problems which represent a generalization of the standard linear complementarity problems. We also study the properties of the model and show that the interior-point methods can be efficiently used for the numerical solutions of the homogenous problem. The second part of the thesis is concerned with a computational study on the use of an optimization-based method in the simulation of fuel motion in a pebble bed reactor. The performance of several optimization packages (BLMVM, TRON, OOQP, and Mosek) for quadratic problems needed to simulate the system is investigated and reported. OOQP will be presented with both the default solver MA27 and our implementation based on CHOLMOD. CHOLMOD-based OOQP version is the fastest of all the packages tested. It consistently uses only about three times more memory than BLMVM, while achieving far higher precision levels. Both solvers behave predictably with the number of pebbles and can be used as robust software solutions in the simulation of the pebble bed reactor.