| Summary: | 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.
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