Optimal solutions to a class of nonconvex minimization problems with linear inequality constraints

Abstract This paper presents a canonical duality theory and optimal solutions to a class of global optimization problems subjected to linear inequality constraints. By using the canonical dual transformation developed recently, a canonical dual problem is formulated, which is perfectly dual to the primal problem. The global minmizer can be identified by the triality theory. Results show that if the global extrema of the original problem are located on the boundary of the primal feasible space, the dual solution should be interior point of the dual feasible set. Several examples are illustrated to show how this theory works.