Article history: Received 28 July 2007 Received in revised form 30 April 2008 Accepted 1 May 2008 Available online 9 May 2008

In this paper, a trust region method for generalized semi-infinite programming problems is presented. The method is based on [O. Yi-gui, “A filter trust region method for solving semi-infinite programming problems”, J. Appl. Math. Comput. 29, 311 (2009)]. We transformed the method from standard to generalized semi-infinite programming problems. The semismooth reformulation of the Karush–Kuhn–Tu...

Semi-Markov decision processes on Borel spaces with deterministic kernels have many practical applications, particularly in inventory theory. Most of the results from general semi-Markov decision processes do not carry over to a deterministic kernel since such a kernel does not provide “smoothness.” We develop infinite dimensional linear programming theory for a general stochastic semi-Markov d...

In this paper, we propose a duality theory for semi-infinite linear programming problems under uncertainty in the constraint functions, the objective function, or both, within the framework of robust optimization. We present robust duality by establishing strong duality between the robust counterpart of an uncertain semi-infinite linear program and the optimistic counterpart of its uncertain La...

This paper provides sufficient conditions for the optimal value function of a given linear semi-infinite programming problem to depend linearly on the size of the perturbations, when these perturbations are directional, involve either the cost coefficients or the right-hand-side function or both, and they are sufficiently small. Two kinds of partitions are considered. The first one concerns the...

Finite-dimensional linear programs satisfy strong duality (SD) and have the “dual 8 pricing” (DP) property. The (DP) property ensures that, given a sufficiently small perturbation of 9 the right-hand-side vector, there exists a dual solution that correctly “prices” the perturbation by 10 computing the exact change in the optimal objective function value. These properties may fail in 11 semi-inf...