AN EXACT PENALIZATION VIEWPOINT OF CONSTRAINED OPTIMIZATION

In their seminal papers Eremin [Soviet Mathematics Doklady, 8 1966), pp. 459-462] and Zangwill [Management Science, 13 (1967), pp. 344-358] introduce a notion of exact penalization for use in the development of algorithms for constrained optimization. Since that time, exact penalty functions have continued to play a key role in the theory of mathematical programming. In the present paper, this theory is unified by showing how the Eremin-Zangwill exact penalty functions can be used to develop the foundations of the theory of constrained optimization for finite dimensions in an elementary and straightforward way. Regularity conditions, multiplier rules, second-order optimality conditions, and convex programming are all given interpretations relative to the Eremin-Zangwill exact penalty functions. In conclusion, a historical review of those results associated with the existence of an exact penalty parameter is provided.