A Global Optimization Technique for Solving a Nonlinear Programming Problem with Equality and Inequality Constraints and Its Application to the Bilevel Programming Problem.

概要

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A global optimization technique is proposed for solving a nonlinear programming problem with equality and inequality constraints by using the concept of exterior penalty method. The original problem is transformed into an auxiliary problem which is an optimization problem with inequality constraints only. It is proved that the global optimal solution can be obtained as an accumulation point of a sequence of solutions to the auxiliary problems, as the penalty parameter goes to the infinite. Under appropriate assumptions, we show that the auxiliary problem can be equivalently transformed to a concave program for which we can find a global optimal solution.It is then applied to solve the bilevel programming problem. We replace the low-level problem by its Kuhn-Tucker conditions, and obtain a nonlinear programming problem with equality and inequality constraints. Then, by applying the above technique, a global optimal solution to the bilevel programming problem is found in the case of convex quadratic lower-level problem.
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