Complete Solutions to General Box-Constrained Global Optimization Problems

[摘要] This paper presents a global optimization method for solving general nonlinear programmingproblems subjected to box constraints. Regardless of convexity or nonconvexity, by introducing adifferential flow on the dual feasible space, a set of complete solutions to the original problem is obtained,and criteria for global optimality and existence of solutions are given. Our theorems improve andgeneralize recent known results in the canonical duality theory. Applications to a class of constrainedoptimal control problems are discussed. Particularly, an analytical form of the optimal control isexpressed. Some examples are included to illustrate this new approach.

[学科分类] 应用数学