Show that the set is convex if and only if its intersection with any line is convex. Show that the convex hull of the $S$ set is the intersection of all convex sets ...

The problem is considered of maximizing a function in a convex region. To solve this problem a new method is developed, to be called "method of feasible directions". It is a method of steep ascent.

Quasiconvex functions play an important role in several branches of applied mathematics (e.g. mathematical programming, minimax theory, games theory, etc.) and of economic analysis (production theory, ...

Abstract: We propose a general recurrent neural-network (RNN) model for nonlinear optimization over a nonempty compact convex subset which includes the bound subset and spheroid subset as special ...

Abstract: We consider a fundamental problem in the field of machine learning-structural risk minimization, which can be represented as the average of a large number of smooth component functions plus ...