Abstract Modelling real processes often results in several suitable models. In order to be able distinguish, or discriminate, which model best represents a phenomenon, one is interested, e.g., so-called T-optimal designs. These consist of the (design) points from generally continuous design space at models deviate most each other under condition that they are fitted those points. Thus, T-criter...

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...

Necessary optimality conditions for a nonsmooth semi-infinite interval-valued vec- tor programming problem are given in the paper by Jennane et al . ( RAIRO:OR (2020). DOI: 10.1051/ro/2020066 ). Having noticed inconsistencies their paper, Gadhi and Ichatouhane 10.1051/ro/2020107 ) made necessary corrections proposed what they considered more pertinent formulation of main Theorem. Recently, 10.1...

In this paper, the equivalence relation between a semi-infinite quadratically constrained convex quadratic programming problem and a combined semidefinite and semi-infinite programming problem is considered. Then, an efficient and reliable discretization algorithm for solving a general class of combined semidefinite and semi-infinite programming problems is developed. Both the continuoustime en...

Set-membership estimation is in general referred in literature as the deterministic approach to state estimation, since its solution can be formulated in the context of set-valued calculus and no stochastic calculations are necessary. This turns out not to be entirely true. In this paper, we show that set-membership estimation can be equivalently formulated in the stochastic setting by employin...

In Machine Learning algorithms, one of the crucial issues is the representation of the data. As the given data source become heterogeneous and the data are large-scale, multiple kernel methods help to classify “nonlinear data”. Nevertheless, the finite combinations of kernels are limited up to a finite choice. In order to overcome this discrepancy, a novel method of “infinite” kernel combinatio...

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...

In this paper we propose a new exchange method for solving convex semi-infinite programming (CSIP) problems. We introduce a new dropping-rule in the proposed exchange algorithm, which only keeps those active constraints with positive Lagrange multipliers. Moreover, we exploit the idea of looking for η-infeasible indices of the lower level problem as the adding-rule in our algorithm. Hence the a...

Here is a (possibly infinite) index set, R 1⁄4 R [ fþ1g [ f 1g denotes the extended real line, f : R ! R and g : R !R. The above optimization problem is performed in the finite-dimensional space R and, if the index set is infinite, is a subject to an infinite number of constraints, therefore it is referred to as a SIP problem. There are numerous applications which lead to SIP problems. We can r...