In this paper, we study a class of fractional semi-infinite polynomial programming problems involving sos-convex functions. For such problem, by conic reformulation proposed in our previous work and the quadratic modules associated with index set, hierarchy semidefinite (SDP) relaxations can be constructed convergent upper bounds optimum obtained. introducing Lasserre’s measure-based representa...

A probabilistic constrained stochastic programming model is formulated, where one term in the objective function, to be minimized, is the maximum of a finite or infinite number of linear functions. The model is reformulated as a finite or semiinfinite disjunctive programming problem. Duality relationships are established for both the original and the convexified problems. Numerical solution tec...

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 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 ...

This paper deals with a nonlinear multiobjective semi-infinite programming problem involving generalized (C,α, ρ, d)-convex functions. We obtain sufficient optimality conditions and formulate the Mond-Weirtype dual model for the nonlinear multiobjective semi-infinite programming problem. We also establish weak, strong and strict converse duality theorems relating the problem and the dual problem.

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...

In this paper we consider min-max convex semi-infinite programming. In order to solve these problems we introduce a unified framework concerning Remez-type algorithms and integral methods coupled with penalty and smoothing methods. This framework subsumes well-known classical algorithms, but also provides some new methods with interesting properties. Convergence of the primal and dual sequences...