Browsing Combinatorics and Optimization by Supervisor "Wolkowicz, Henry"
Now showing items 18 of 8

ADMM for SDP Relaxation of GP
(University of Waterloo, 20160830)We consider the problem of partitioning the set of nodes of a graph G into k sets of given sizes in order to minimize the cut obtained after removing the kth set. This is a variant of the wellknown vertex separator ... 
A Blueprint for Semidefinite Relaxations of BinaryConstrained Quadratic Programs Computing tight bounds on NPhard problems using ADMM
(University of Waterloo, 20201218)This thesis looks at the solution techniques of two NPhard, large scale problems, the quadratic assignment problem, QAP, and the side chain positioning, SCP, problem. We summarize existing approaches from and look at the ... 
Comparing Classical Portfolio Optimization and Robust Portfolio Optimization on Black Swan Events
(University of Waterloo, 20210129)Black swan events, such as natural catastrophes and manmade market crashes, historically have a drastic negative influence on investments; and there is a discrepancy on losses caused by these two types of disasters. In ... 
Error Bounds and Singularity Degree in Semidefinite Programming
(University of Waterloo, 20200124)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, 20230309)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 ... 
Nonsmooth Newton Methods for Solving the Best Approximation Problem; with Applications to Linear Programming
(University of Waterloo, 20231219)In this thesis, we study the effects of applying a modified LevenbergMarquardt regularization to a nonsmooth Newton method. We expand this application to exact and inexact nonsmooth Newton methods and apply it to the ... 
Semidefinite Programming Relaxations of the Simplified Wasserstein Barycenter Problem: An ADMM Approach
(University of Waterloo, 20230504)The Simplified Wasserstein Barycenter problem, the problem of picking k points each chosen from a distinct set of n points as to minimize the sum of distances to their barycenter, finds applications in various areas of ... 
Sensitivity Analysis and Robust Optimization: A Geometric Approach for the Special Case of Linear Optimization
(University of Waterloo, 20181221)In this thesis, we study the special case of linear optimization to show what may affect the sensitivity of the optimal value function under data uncertainty. In this special case, we show that the robust optimization ...