عنوان

Conic Optimization:

Number

TLpq2187635276

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

Conic Optimization:

General Material Designation

[Thesis]

First Statement of Responsibility

Mohammad-Nezhad, Ali

Title Proper by Another Author

Optimal Partition, Parametric, and Stability Analysis

Subsequent Statement of Responsibility

Terlaky, Tamas

Name of Publisher, Distributor, etc.

Lehigh University

Date of Publication, Distribution, etc.

2019

Specific Material Designation and Extent of Item

294

Dissertation or thesis details and type of degree

Ph.D.

Body granting the degree

Lehigh University

Text preceding or following the note

2019

Text of Note

A linear conic optimization problem consists of the minimization of a linear objective function over the intersection of an affine space and a closed convex cone. In recent years, linear conic optimization has received significant attention, partly due to the fact that we can take advantage of linear conic optimization to reformulate and approximate intractable optimization problems. Steady advances in computational optimization have enabled us to approximately solve a wide variety of linear conic optimization problems in polynomial time. Nevertheless, preprocessing methods, rounding procedures and sensitivity analysis tools are still the missing parts of conic optimization solvers. Given the output of a conic optimization solver, we need methodologies to generate approximate complementary solutions or to speed up the convergence to an exact optimal solution. A preprocessing method reduces the size of a problem by finding the minimal face of the cone which contains the set of feasible solutions. However, such a preprocessing method assumes the knowledge of an exact solution. More importantly, we need robust sensitivity and post-optimal analysis tools for an optimal solution of a linear conic optimization problem. Motivated by the vital importance of linear conic optimization, we take active steps to fill this gap. This thesis is concerned with several aspects of a linear conic optimization problem, from algorithm through solution identification, to parametric analysis, which have not been fully addressed in the literature. We specifically focus on three special classes of linear conic optimization problems, namely semidefinite and second-order conic optimization, and their common generalization, symmetric conic optimization. We propose a polynomial time algorithm for symmetric conic optimization problems. We show how to approximate/identify the optimal partition of semidefinite optimization and second-order conic optimization, a concept which has its origin in linear optimization. Further, we use the optimal partition information to either generate an approximate optimal solution or to speed up the convergence of a solution identification process to the unique optimal solution of the problem. Finally, we study the parametric analysis of semidefinite and second-order conic optimization problems. We investigate the behavior of the optimal partition and the optimal set mapping under perturbation of the objective function vector.

Applied Mathematics

Operations research

Mohammad-Nezhad, Ali

Terlaky, Tamas

Electronic name

p

[Thesis]

276903

a

Y