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 our previous work we have discussed the valence band electronic band structure of a (001) oriented surface (semi–infinite medium) of some II–VI and III–V zinc–blende semiconductor compounds. For these systems, we have found three characteristic surface resonances, besides the known bulk bands (hh, lh and spin–orbit bands). Two of these resonances correspond to the anion terminated surface an...

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 ...

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.

The reflection from and transmission through a semi-infinite chiral medium are analyzed by obtaining the Fresnel equations in terms of paralleland perpendicular-polarized modes, and a comparison is made with results reported previously. The chiral medium is described electromagnetically by the constitutive relations D = EE + i-yB and H = i-yE + (1/,)B. The constants , u, and -y are real and hav...

In this paper we are interested with a strongly coupled system of partial differential equations that modelizes free convection in a two-dimensional bounded domain filled with a fluid saturated porous medium. This model is inspired by the one of free convection near a semi-infinite impermeable vertical flat plate embedded in a fluid saturated porous medium. We establish the existence and unique...

Time-resolved Fourier optical diffuse tomography is a novel approach for imaging of objects in a highly scattering turbid medium with use of an incident (near) plane wave. The theory of the propagation of spatial Fourier components of the scattered wave field is presented, along with a fast algorithm for three-dimensional reconstruction in a parallel planar geometry. Examples of successful reco...

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...