In this paper we study first order optimality conditions for the class of generalized semi-infinite programming problems (GSIPs). We extend various wellknown constraint qualifications for finite programming problems to GSIPs and analyze the extent to which a corresponding Karush-Kuhn-Tucker (KKT) condition depends on these extensions. It is shown that in general the KKT condition for GSIPs take...

We present computationally efficient and accurate semiempirical models of light transfer suitable for real-time diffuse reflectance spectroscopy. The models predict the diffuse reflectance of both (i) semi-infinite homogeneous and (ii) two-layer media exposed to normal and collimated light. The two-layer medium consisted of a plane-parallel slab of finite thickness over a semi-infinite layer wi...

‎linear semi-infinite programming problem is an important class of optimization problems which deals with infinite constraints‎. ‎in this paper‎, ‎to solve this problem‎, ‎we combine a discretization method and a neural network method‎. ‎by a simple discretization of the infinite constraints,we convert the linear semi-infinite programming problem into linear programming problem‎. ‎then‎, ‎we use...

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.

The propagation of electromagnetic radiation in periodically stratified media is considered. Media of finite, semi-infinite, and infinite extent are treated. A diagonalization of the unit cell translation operator is used to obtain exact solutions for the Bloch waves, the dispersion relations, and the band structure of the medium. Some new phenomena with applications to integrated optics and la...