Fast, Globally Convergent Optimization Algorithms, with Application to Engineering System Design

Abstract

Complex engineering system design usually involves multiple objective specifications. Tradeoffs have to be made among these specifications, possibly under constraints, as they oftentimes compete with one another. It has been realized that these problems can be faithfully translated into (inequality) constrained minimax problems, or a sequence of such problems and then the originally design problems can be solved with the support of numerical optimization techniques. This dissertation develops a number of optimization algorithms for the solution of these problems, with emphasis on many distinctive features of engineering systems that existing optimization algorithms have not fully exploited or accounted for. Efforts are made to maintain "desirable" analytic properties that existing popular optimization algorithms enjoy.Algorithms are developed in a very general setup, yet specialized to indicate the direct connections with different branches of engineering applications. The adaptation of advanced optimization techniques, such as feasible sequential quadratic programming (FSQP) and nonmonotone line search (NLS), to the solution of engineering problems are carefully addressed. Efficiency of these algorithms has been given high priority in the development, since it is usually very time-consuming to evaluate specifications in engineering applications.In the presence of functional specifications, i.e., specifications that are to be satisfied over an interval of a free parameter such as time or frequency (shaping of time or frequency response, for instance), an efficient algorithm is proposed that significantly outperforms the existing algorithms in the same context. This algorithm has been successfully applied for the solution of many engineering problems in the context of optimization-based system design.These new algorithms are satisfactorily characterized by conventional notions of optimization such as global convergence and rate of local convergence. Interesting and meaningful results on the rate of local convergence are obtained with the aid of nonmonotone line search. The performance of these algorithms represented by extensive numerical experiments measures up to the theoretic analysis.A number of feedback system design problems are provided to illustrate the efficiency and applicability of these algorithms.