PRIMAL-RELAXED DUAL GLOBAL OPTIMIZATION APPROACH

A deterministic global optimization approach is proposed for nonconvex constrained nonlinear programming problems. Partitioning of the varia bles, along with the introduction of transformation variables, if nece ssary, converts the original problem into primal and relaxed dual subp roblems that provide valid upper and lower bounds respectively on the global optimum. Theoretical properties are presented which allow for a rigorous solution of the relaxed dual problem. Proofs of epsilon-fini te convergence and epsilon-global optimality are provided. The approac h is shown to be particularly suited to (a) quadratic programming prob lems, (b) quadratically constrained problems, and (c) unconstrained an d constrained optimization of polynomial and rational polynomial funct ions. The theoretical approach is illustrated through a few example pr oblems. Finally, some further developments in the approach are briefly discussed.