the rapid melting of a semi- infinite body due to the absorption of a cw laser beam radiation has been studied. the enthalpy technique for the solution of phase change problems has been used in an explicit finite difference form to calculate the transient temperature distribution in the semi-infinite body and the growth rate of the melt pool. the technique has been modified so that it is not ne...

‎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...

By considering the epigraphs of conjugate functions, we extend the Fenchel duality, applicable to a (possibly infinite) family of proper lower semicontinuous convex functions on a Banach space. Applications are given in providing fuzzy KKT conditions for semi-infinite programming.

In this work, we develop duality of the minimum volume circumscribed ellipsoid and the maximum volume inscribed ellipsoid problems. We present a unified treatment of both problems using convex semi–infinite programming. We establish the known duality relationship between the minimum volume circumscribed ellipsoid problem and the optimal experimental design problem in statistics. The duality res...

In this note we are concerned with the generalization given by Ferris and Philpott [3] of the affine scaling algorithm discovered by Dikin [2] to solve semi-infinite linear programming problems, in which the number of variables is finite, but the number of constraints is not. In [3] a discrepancy is pointed out between the classical algorithm and its generalization. The purpose of this note is ...