A hybrid optimization method and its role in computer-aided design

The variable metric methods have been analyzed and exploited in the past to achieve a superlinear rate of convergence in unconstrained optimization. Recently, the update formulas used in these methods have been extended for constrained optimization. The update formulas construct approximate second order derivatives using first order information. These are referred to as constrained variable metric (CVM) methods. Higher order of convergence is often accompanied by a smaller domain of convergence. To overcome this limitation of CVM methods, a hybrid optimization algorithm is presented in this paper. It uses a cost function bounding concept initially and a CVM method in later stages of the search process. In addition, the algorithm uses an active set strategy and is globally convergent. An improved active set strategy is suggested. Besides developing a superlinear optimization algorithm, an efficient programming structure for computer-aided design of engineering systems is suggested and implemented. A number of mathematical programming problems, and small and large scale engineering design problems are solved to test numerical aspects of the algorithm. The algorithm has performed extremely well on the test problems.