Browsing University of Waterloo by Supervisor "Tuncel, Levent"
Now showing items 1-6 of 6
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Comparing Intersection Cut Closures using Simple Families of Lattice-Free Convex Sets
(University of Waterloo, 2022-04-26)Mixed integer programs are a powerful mathematical tool, providing a general model for expressing both theoretically difficult and practically useful problems. One important subroutine of algorithms solving mixed integer ... -
Convex Optimization via Domain-Driven Barriers and Primal-Dual Interior-Point Methods
(University of Waterloo, 2017-08-24)This thesis studies the theory and implementation of infeasible-start primal-dual interior-point methods for convex optimization problems. Convex optimization has applications in many fields of engineering and science such ... -
Inner approximation of convex cones via primal-dual ellipsoidal norms
(University of Waterloo, 2016-05-13)We study ellipsoids from the point of view of approximating convex sets. Our focus is on finding largest volume ellipsoids with specified centers which are contained in certain convex cones. After reviewing the related ... -
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 ... -
On Polynomial-time Path-following Interior-point Methods with Local Superlinear Convergence
(University of Waterloo, 2016-09-30)Interior-point methods provide one of the most popular ways of solving convex optimization problems. Two advantages of modern interior-point methods over other approaches are: (1) robust global convergence, and (2) the ... -
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 ...