A necessary condition - the Principle of Fermat-Lagrange - is offered for mixed smooth-convexoptimization problems. This generalizes and unifies most of the known necessary conditions forconcrete finite and infinite dimensional optimization problems of interest. The new idea in comparisonwith...

We consider infinite products of the form ,where {mk} is an arbitrary sequence of trigonometric polynomials of degree at most n with uniformly bounded normssuch that mk(0)=1 for all k. We show that can decrease at infinity not faster than and present conditions underwhich this maximal decay...