AUGMENTED LAGRANGIAN METHODS FOR A CLASS OF LARGE-SCALE CONIC PROGRAMMING

Abstract

In this thesis, we design, analyze and implement efficient algorithms for solving a class of large-scale conic programming (CQP) problems which are fundamental problems in the field of mathematical optimization. These problems also arise from many important real-world applications. The thesis can be divided mainly into four parts. The first part of this thesis focuses on the augmented Lagrangian method for solving convex quadratic programming problems with linear and conic constraints. In the second part of the thesis, we consider solving a special class of CQP, namely second-order cone programming, which has many important real-world applications and is of independent interest by the non-polyhedral nature of the underlying second-order cone. Next, we consider the doubly nonnegative projection problem which aims to compute the projection onto the doubly nonnegative cone. In the last part of the thesis, we aim to solve large-scale convex quadratic programming problems.