Control System Approach for Constructing Numerical Methods in Optimization and Applications

Abstract

This thesis presents newly developed numerical methods based on bang-bang iterations. They are formulated using a component-wise line search strategy which results in a sequence of rectangular search regions. To obtain a long-term optimal trajectory, a two-phase approach is also incorporated to solve unconstrained and equality constrained optimization problems. To ensure convergence, a backtracking line search is used to satisfy the Lyapunov function theorem where monotonic decrement of the function value is ensured.