Interior-point methods and stability in optimization

• Main Author: Beyko, Taras.
• Format: Others
• Language: en
• Published: McGill University 1999
• Subjects: Mathematics.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=30342

This thesis is a study of stability and numerical methods in optimization and control systems. Our first goal is to investigate different types of stability: continuity of the feasible set mapping, stability and controllability of dynamical systems and control processes, and stability of numerical algorithms. The second goal is implementation of polynomial-time algorithms for solving problems of optimization, stabilization, modelling, and input optimization of control systems. We are using polynomial-time interior-point methods and analytic center cutting plane methods. In particular, we study relations between abstract optimization problems and their finite-dimensional discretizations.