This paper deals with approximate solutions of a nonsmooth semi-infinite programming multiple interval-valued objective functions. We first introduce four types quasi Pareto the considered problem by considering lower-upper interval order relation and then apply some advanced tools variational analysis generalized differentiation to establish necessary optimality conditions for these solutions....

A dual convex programming approach to solving linear programs with inequality constraints through entropic perturbation is derived. The amount of perturbation required depends on the desired accuracy of the optimum. The dual program contains only non-positivity constraints. An eoptimal solution to the linear program can be obtained effortlessly from the optimal solution of the dual program. Sin...

Several characterizations of solution sets of a class of convex infinite programs are given using Lagrange multiplier conditions. The results are then applied to some classes of optimization problems: cone-constrained convex programs and fractional programs. A class of semi-convex problems with convex constraints are also examined. Optimality conditions are obtained and several characterization...

This paper is concerned with the Lipschitzian behavior of the optimal set of convex semi-infinite optimization problems under continuous perturbations of the right hand side of the constraints and linear perturbations of the objective function. In this framework we provide a sufficient condition for the metric regularity of the inverse of the optimal set mapping. This condition consists of the ...

The Fourier-Motzkin elimination method has been recently extended to linear inequality systems that have infinitely many inequalities. It has been used in the study of linear semi-infinite programming by Basu, Martin, and Ryan. Following the idea of the conjecture for semi-infinite programming in a paper by Kortanek and Zhang recently published in Optimization, which states “all the duality res...

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm,  such that $f + g $ attains its strong minimum on $X. $ This result extends some of the  well-known varitional principles as that of Ekeland [On the variational principle,  J. Ma...

We propose an approach to find the optimal value of a convex semi-infinite program (SIP) that involves identifying finite set relevant constraints by solving finite-dimensional global maximization problem. One major advantages our is it admits plug-and-play module where any suitable optimization algorithm can be employed obtain SIP. As example, we simulated annealing based which useful especial...

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...

in this paper, we deal to obtain some new complexity results for solving semidefinite optimization (sdo) problem by interior-point methods (ipms). we define a new proximity function for the sdo by a new kernel function. furthermore we formulate an algorithm for a primal dual interior-point method (ipm) for the sdo by using the proximity function and give its complexity analysis, and then we sho...