Browsing Combinatorics and Optimization by Subject "linear programming"
Now showing items 1-7 of 7
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Algorithmic and Linear Programming-Based Techniques for the Maximum Utility Problem
(University of Waterloo, 2023-05-25)A common topic of study in the subfield of Operations Research known as Revenue Management is finding optimal prices for a line of products given customer preferences. While there exists a large number of ways to model ... -
Computing the Nucleolus of Matching and b-Matching Games
(University of Waterloo, 2021-05-21)In the classical weighted matching problem the optimizer is given a graph with edge weights and their goal is to find a matching which maximizes the sum of the weights of edges in the matching. It is typically assumed in ... -
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 ... -
Nonsmooth Newton Methods for Solving the Best Approximation Problem; with Applications to Linear Programming
(University of Waterloo, 2023-12-19)In this thesis, we study the effects of applying a modified Levenberg-Marquardt regularization to a nonsmooth Newton method. We expand this application to exact and inexact nonsmooth Newton methods and apply it to the ... -
Polyhedral Diameters and Applications to Optimization
(University of Waterloo, 2022-09-01)The Simplex method is the most popular algorithm for solving linear programs (LPs). Geometrically, it moves from an initial vertex solution to an improving neighboring one, selected according to a pivot rule. Despite decades ... -
Relaxations of the Maximum Flow Minimum Cut Property for Ideal Clutters
(University of Waterloo, 2021-01-29)Given a family of sets, a covering problem consists of finding a minimum cost collection of elements that hits every set. This objective can always be bound by the maximum number of disjoint sets in the family, we refer ... -
Sensitivity Analysis and Robust Optimization: A Geometric Approach for the Special Case of Linear Optimization
(University of Waterloo, 2018-12-21)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 ...