A unified quadratic semi-infinite programming approach is introduced to solve digital filter design problems with time or frequency-domain specification. An algorithm based on this approach is developed and the corresponding convergence result is presented. This computational method is then applied to the optimum filter design problems subject to time and frequency domain specifications, namely...

This paper is devoted to the study of perturbed semi-infinite optimization problems, i.e., minimization over ]R with an infinite number of inequality constraints. We obtain the second-order expansion of the optimal value function and the first-order expansion of approximate optimal solutions in two cases: (i) when the number of binding constraints is finite and (ii) when the inequality constrai...

In this paper new results are established in multiobjective DC programming with infinite convex constraints (MOPIC for abbr.) that are defined on Banach space (finite or infinite) with objectives given as the difference of convex functions subject to infinite convex constraints. This problem can also be called multiobjective DC semi-infinite and infinite programming, where decision variables ru...

In this paper, we propose a duality theory for semi-infinite linear programming problems under uncertainty in the constraint functions, the objective function, or both, within the framework of robust optimization. We present robust duality by establishing strong duality between the robust counterpart of an uncertain semi-infinite linear program and the optimistic counterpart of its uncertain La...

Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound ...

This paper presents a new practical approach to complex quadratic programming which solves the broad class of complex approximation problems employing finitization of semi-infinite formulations. The approximation problem may be general with arbitrarily complex basis functions. By using a new technique, the associated semi-infinite quadratic programming problem can be solved taking advantage of ...

This paper is devoted to the investigation of optimality conditions and saddle point theorems for robust approximate quasi-weak efficient solutions a nonsmooth uncertain multiobjective fractional semi-infinite optimization problem (NUMFP). Firstly, necessary condition established by using properties Gerstewitz’s function. Furthermore, kind pseudo/quasi-convex function defined (NUMFP), under its...

We analyse model problems of stress-induced atomic diffusion from a point source or from the surface of a material into an infinite or semi-infinite grain boundary, respectively. The problems are formulated in terms of partial differential equations which involve singular integral operators. The self-similarity of these equations leads to singular integro-differential equations which are solved...