The Reformulation-Linearization Technique (RLT) provides a hierarchy of relaxations spanning the spectrum from the continuous relaxation to the convex hull representation for linear 0-1 mixed-integer and general mixed-discrete programs. We show in this paper that this result holds identically for semi-infinite programs of this type. As a consequence, we extend the RLT methodology to describe a ...

We introduce a new numerical solution method for semi-infinite optimization problems with convex lower level problems. The method is based on a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized nonlinear complementarity problem functions. This approach leads to central path conditions for the lower level problems, where for a given path parameter a smoo...

A new approach is presented to obtain a convex set of robust D—stabilizing fixed structure controllers, relying on Cauchy's argument principle. controllers around an initial controller for multi-model represented by infinite Linear Matrix Inequalities (LMIs). By appropriate sampling the D—stability boundary, Semi-Definite Programming (SDP) proposed that can be integrated in other synthesis appr...

The BCQ and the Abadie CQ for infinite systems of convex inequalities in Banach spaces are characterized in terms of the upper semi-continuity of the convex cones generated by the subdifferentials of active convex functions. Some relationships with other constraint qualifications such as the CPLV and the Slate condition are also studied. Applications in best approximation theory are provided.

In this paper we describe how robot trajectory planning can be formulated as a semi-infinite programming (SIP) problem. The formulation as a SIP problem allowed us to treat the problem with one of the three main classes of methods for solving SIP, the discretization class. Two of the robotics trajectory planning problems formulated were coded in the SIPAMPL [1] environment which is publicly ava...

Model reduction of high order linear-in-parameters discrete-time systems is considered. The main novelty of the paper is that the coefficients of the original system model are assumed to be known only within given intervals, and the coefficients of the derived reduced order model are also obtained in intervals, such that the complex value sets of the uncertain original and reduced models will b...

This paper contains selected applications of the new tangential extremal principles and related results developed in [20] to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraints.

This paper introduces a global approach to the semi-infinite programming problem that is based upon a generalisation of the g~ exact penalty function. The advantages are that the ensuing penalty function is exact and the penalties include all violations. The merit function requires integrals for the penalties, which provides a consistent model for the algorithm. The discretization is a result o...

The discretization approach for solving semi-infinite optimization problems is considered. We are interested in the rate of the approximation error between the solution of the semi-infinite problem and the solution of the discretized program depending on the discretization mesh-size d. It will be shown how this rate depends on whether the minimizer is strict of order one or two and on whether t...

Fourier-Motzkin elimination is a projection algorithm for solving finite linear programs. Weextend Fourier-Motzkin elimination to semi-infinite linear programs which are linear programswith finitely many variables and infinitely many constraints. Applying projection leads to newcharacterizations of important properties for primal-dual pairs of semi-infinite programs suchas zero ...