On the Role of Continuously Differentiable Exact Penalty Functions in Constrained Global Optimization.

The aim of this paper is to show that the new continuously differentiable exact penalty functions recently proposed in literature can play an important role in the field of constrained global optimization. In fact they allow us to transfer ideas and results proposed in unconstrained global optimization to the constrained case. First, by drawing our inspiration from the unconstrained case and by using the strong exactness properties of a particular continuously differentiable penalty function, we propose a sufficient condition for a local constrained minimum point to be global. Then we show that every constrained local minimum point satisfying the second order sufficient conditions is an ldquoattraction pointrdquo for a particular implementable minimization algorithm based on the considered penalty function. This result can be used to define new classes of global algorithms for the solution of general constrained global minimization problems. As an example, in this paper we describe a simulated annealing algorithm which produces a sequence of points converging in probability to a global minimum of the original constrained problem.