Browsing Combinatorics and Optimization by Subject "semidefinite programming"
Now showing items 1-6 of 6
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A Comprehensive Analysis of Lift-and-Project Methods for Combinatorial Optimization
(University of Waterloo, 2014-08-20)In both mathematical research and real-life, we often encounter problems that can be framed as finding the best solution among a collection of discrete choices. Many of these problems, on which an exhaustive search in the ... -
Error Bounds and Singularity Degree in Semidefinite Programming
(University of Waterloo, 2020-01-24)An important process in optimization is to determine the quality of a proposed solution. This usually entails calculation of the distance of a proposed solution to the optimal set and is referred to as forward error. ... -
Implicit Loss of Surjectivity and Facial Reduction: Theory and Applications
(University of Waterloo, 2023-03-09)Facial reduction, pioneered by Borwein and Wolkowicz, is a preprocessing method that is commonly used to obtain strict feasibility in the reformulated, reduced constraint system. The importance of strict feasibility is ... -
Low-Rank Plus Sparse Decompositions of Large-Scale Matrices via Semidefinite Optimization
(University of Waterloo, 2023-05-19)We study the problem of decomposing a symmetric matrix into the sum of a low-rank symmetric positive semidefinite matrix and a tridiagonal matrix, and a relaxation which looks for symmetric positive semidefinite matrices ... -
Mathematical Programming Formulations of the Planar Facility Location Problem
(University of Waterloo, 2007-09-24)The facility location problem is the task of optimally placing a given number of facilities in a certain subset of the plane. In this thesis, we present various mathematical programming formulations of the planar ... -
Preprocessing and Reduction for Semidefinite Programming via Facial Reduction: Theory and Practice
(University of Waterloo, 2013-11-26)Semidefinite programming is a powerful modeling tool for a wide range of optimization and feasibility problems. Its prevalent use in practice relies on the fact that a (nearly) optimal solution of a semidefinite program ...