Certain Nondifferentiable Constrained Optimization Problem Of The Approximate Function Method

This dissertation is devoted to some numerical methods for solving optimization problems in the management science and engineering setting. The methods we concern with are the maximum entropy method and smooth approximating function method;and the main work of the dissertation can be summarized as follows:1. The semi-infinite min-max problem often appears in an engineering design setting.A maximum entropy method based algorithm for semi-infinite mix-max problems with equality and/or inequality constraints are established. Properties of the method are studied and its convergence is proven. Numerical results are presented which show that the method is effective.2. The nonlinear l₁ problem is an important non-differentiable optimization problem. It is of great practical importance to network and system design.A smooth approximating algorithm is proposed to study the non-differentiable constrained nonlinear l₁ problem. This method attempts to overcome some drawbacks of former methods especially the maximum entropy method.The algorithm is global convergent under mild conditions. Primary numerical results demonstrate that the algorithm is efficient.3. An efficient algorithm for solving nonlinear programming is presented by applying the smooth approximating function.The algorithm is based on a differ-entiable and "almost" exact penalty function and a successive approximation tech-nique.The solution error of subproblems can be controlled by selecting suitable pa-rameters. Preliminary numerical experiments show that the proposed algorithm is effective.