We consider an optimization problem for spatial power distribution generated by an array of transmitting elements. Using ultrasound hyperthermia cancer treatment as a motivating example, the signal design problem consists of optimizing the power distribution across the tumor and healthy tissue regions, respectively. The models used in the optimization problem are, however, invariably subject to...

The purpose of this paper is to consider the Mond-Weir type dual model for a class of non-smooth multiobjective semi-infinite programming problem. In this work, we use generalization of convexity namely ( , ) G F θ − convexity and Kuhn-Tucker constraint qualification, to prove new duality results for such semi-infinite programming problem. Weak, strong and converse duality theorems are derived....

Generalized semi-infinite optimization problems (GSIP) are considered. The difference between GSIP and standard semi-infinite problems (SIP) is illustrated by examples. By applying the ’Reduction Ansatz’, optimality conditions for GSIP are derived. Numerical methods for solving GSIP are considered in comparison with methods for SIP. From a theoretical and a practical point of view it is investi...

We consider a generalized semi-infinite programming problem (GSIP) with one semi-infinite constraint where the index set depends on the variable to be minimized. Keeping in mind the integral global optimization method of Zheng & Chew and its modifications we would like to outline theoretical considerations for determining coarse approximations of a solution of (GSIP) via global optimization of ...

A nonconvex generalized semi-infinite programming problem is considered involving parametric max-functions in both, the objective and the constraints. For a fixed vector of parameters, the values of these parametric max-functions are given as optimal values of convex quadratic programming problems. Assuming that for each parameter the parametric quadratic problems satisfy the strong duality rel...

We present efficiently verifiable sufficient conditions for the validity of specific NP-hard semi-infinite systems of semidefinite and conic quadratic constraints arising in the framework of Robust Convex Programming and demonstrate that these conditions are “tight” up to an absolute constant factor. We discuss applications in Control on the construction of a quadratic Lyapunov function for lin...

In contrast to the stochastic differential equation models used for the calculation of the term structure of interest rates, we develop an approach based on linear dynamical systems under non-stochastic uncertainty with perturbations. The uncertainty is described in terms of unknown feasible sets for varying parameters, whose values are otherwise unknown. Observations are used intrinsically in ...

In Machine Learning (ML) algorithms, one of the crucial issues is the representation of the data. As the data become heterogeneous and large-scale, single kernel methods become insufficient to classify nonlinear data. The finite combinations of kernels are limited up to a finite choice. In order to overcome this discrepancy, we propose a novel method of ”infinite” kernel combinations for learni...