We clarify a financial meaning of duality in the semi-infinite programming problem which emerges in the context of determining a derivative price range based only on the no-arbitrage assumption and the observed prices of other derivatives. The interpretation links studies in the above context to studies in stochastic models.

A semi-infinite programming problem is an optimization problem in which finitely many variables appear in infinitely many constraints. This model naturally arises in an abundant number of applications in different fields of mathematics, economics and engineering. The present paper intends to give a short introduction into the field and to present some preliminary discussion on the complexity of...

In this paper, an unconstrained convex programming dual approach for solving a class of linear semi-infinite programming problems is proposed. Both primal and dual convergence results are established under some basic assumptions. Numerical examples are also included to illustrate this approach.

This work presents a stochastic outer approximation algorithm to solve air pollution control problem while minimizing the control costs which thereby occur. These air quality standards give rise to an infinite number of constraints and this is a semi-infinite programming problem.

This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to problems of semi-infinite and infinite programming with feasible solution sets defined by parameterized systems of infinitely many linear inequalities of the type intensively studied in the preceding development [5) from our viewpoint of robust Lipschitzian stability. We present me...

After an introduction to main ideas of semi-infinite optimization, this article surveys recent developments in theory and numerical methods for standard and generalized semi-infinite optimization problems. Particular attention is paid to connections with mathematical programs with complementarity constraints, lower level Wolfe duality, semi-smooth approaches, as well as branch and bound techniq...

In practice, there are many problems which decision parameters are fuzzy numbers, and some kind of this problems are formulated as either possibilitic programming or multi-objective programming methods. In this paper, we consider a multi-objective programming problem with fuzzy data in constraints and introduce a new approach for solving these problems base on a combination of the multi-objecti...

Semi-infinite linear programs often arise as the limit of a sequence of approximating linear programs. Hence, studying the behavior of extensions of linear programming algorithms to semi-infinite problems can yield valuable insight into the behavior of the underlying linear programming algorithm when the number of constraints or the number of variables is very large. In this paper, we study the...

We first present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop an algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. The cutting surface algorithm is also applicable to problems with non-differentiable sem...