In this paper, we will study optimality conditions of semi-infinite programs and generalized semi-infinite programs, for which the gradient objective function when evaluated at any feasible direction for the linearized constraint set is non-negative. We consider three types of penalty functions for semi-infinite program and investigate the relationship among the exactness of these penalty funct...

We shall give a lower estimate of harmonic‎ ‎functions of order greater than one in a half space‎, ‎which‎ ‎generalize the result obtained by B‎. ‎Ya‎. ‎Levin in a half plane‎.

By a counter example we show that two continuous functions defined on a compact metric space satisfying a certain semi metric need not have a common periodic point.

We prove a continuity inheritance property for super- and sub-additive transformations of non-negative continuous multivariate functions defined on the domain of all non-negative points and vanishing at the origin. As a corollary of this result we obtain that super- and sub-additive transformations of continuous aggregation functions are again continuous aggregation functions.

The Douglas–Rachford (DR) and alternating direction method of multipliers (ADMM) are two proximal splitting algorithms designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to compute. The goal of this work is to understand the local linear convergence behaviour of DR/ADMM when the involved functions are moreover partly smooth. More...

We show that the semi-linear ordering principle for continuous functions implies the determinacy of all Wadge and Lipschitz games. c © 2006 Elsevier B.V. All rights reserved.

The concept of a (δ, β)-irresolute function in topological spaces is introduced and studied. Some of their characteristic properties are considered. We also investigate the relationships between these classes of functions and other classes of non-continuous functions. AMS subject classifications: 54C10, 54D10

Radzik (1991) showed that, by strengthening the usual quasi-concavity assumption on players’ payoff functions, upper semi-continuous two-player games on compact intervals of the real line have ε-equilibria for all ε > 0. Ziad (1997) then stated that the same conclusion holds for n-player games on compact, convex subsets of Rm, m ≥ 1, provided that the upper semi-continuity condition is strength...