Extension of the LP-Newton method to conic programming problems via semi-infinite representation

A Smoothing Newton Method for Semi-Infinite Programming

Semi-infinite linear programming approaches to semidefinite programming problems∗

Interior point methods, the traditional methods for the SDP , are fairly limited in the size of problems they can handle. This paper deals with an LP approach to overcome some of these shortcomings. We begin with a semi-infinite linear programming formulation of the SDP and discuss the issue of its discretization in some detail. We further show that a lemma due Pataki on the geometry of the SDP...

Application of general semi-infinite programming to lapidary cutting problems

We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP ) and solved using an interiorpoint method developed by Stein. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of co...

Optimality Conditions for Semi-infinite and Generalized Semi-infinite Programs via lp Exact Penalty Functions

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...

Convex Generalized Semi-Infinite Programming Problems with Constraint Sets: Necessary Conditions

 We consider generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be convex. Considering a lower level constraint qualification, we derive a formula for estimating the subdifferential of the value function. Finally, we establish the Fritz-John necessary optimality con...