David Yang Gao

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This paper presents, within a unified framework, a potentially powerful canonical dual transformation method and associated generalized duality theory in nonsmooth global optimization. It is shown that by the use of this method, many nonsmooth/nonconvex constrained primal problems in R n can be reformulated into certain smooth/convex unconstrained dual(More)
This paper presents a canonical duality theory for solving quadratic minimization problems subjected to either box or integer constraints. Results show that under Gao and Strang's general global optimality condition, these well-known nonconvex and discrete problems can be converted into smooth concave maximization dual problems over closed convex feasible(More)
This paper presents a perfect duality theory and a complete set of solutions to nonconvex quadratic programming problems subjected to inequality constraints. By use of the canonical dual transformation developed recently, a canonical dual problem is formulated, which is perfectly dual to the primal problem in the sense that they have the same set of KKT(More)
This paper presents a set of complete solutions to a class of polynomial optimization problems. By using the so-called sequential canonical dual transformation developed in the author's recent book [Gao, D.Y. xviii + 454 pp], the nonconvex polynomials in R n can be converted into an one-dimensional canonical dual optimization problem, which can be solved(More)
This paper presents a canonical duality theory for solving a general nonconvex 1 quadratic minimization problem with nonconvex constraints. By using the canonical dual 2 transformation developed by the first author, the nonconvex primal problem can be con-3 verted into a canonical dual problem with zero duality gap. A general analytical solution 4 form is(More)
We focus on a comparative study of three recently developed nature-inspired optimization algorithms, including state transition algorithm, harmony search and artificial bee colony. Their core mechanisms are introduced and their similarities and differences are described. Then, a suit of 27 well-known benchmark problems are used to investigate the(More)