On Necessary Conditions for a Minimum

Resumo

We discuss a general approach to necessary optimality conditions based on the so-called “optimality alternative,” which reduces a problem with constraints to an unconstrained problem or a sequence of unconstrained problems. The power of the approach is demonstrated by a proof of a necessary optimality condition in an abstract problem with mixed (convex vs. nonconvex) structure and a new proof of Clarke’s “stratified” maximum principle for optimal control of differential inclusions.