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...

In this paper we consider min-max convex semi-infinite programming. In order to solve these problems we introduce a unified framework concerning Remez-type algorithms and integral methods coupled with penalty and smoothing methods. This framework subsumes well-known classical algorithms, but also provides some new methods with interesting properties. Convergence of the primal and dual sequences...

This paper contains selected applications of the new tangential extremal principles and related results developed in [20] to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraints.

This paper introduces a global approach to the semi-infinite programming problem that is based upon a generalisation of the g~ exact penalty function. The advantages are that the ensuing penalty function is exact and the penalties include all violations. The merit function requires integrals for the penalties, which provides a consistent model for the algorithm. The discretization is a result o...

The discretization approach for solving semi-infinite optimization problems is considered. We are interested in the rate of the approximation error between the solution of the semi-infinite problem and the solution of the discretized program depending on the discretization mesh-size d. It will be shown how this rate depends on whether the minimizer is strict of order one or two and on whether t...

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...

We consider the class of semi-infinite programming problems which became in recent years a powerful tool for the mathematical modelling of many real-life problems. In this paper, we study an augmented Lagrangian approach to semi-infinite problems and present necessary and sufficient conditions for the existence of corresponding augmented Lagrange multipliers. Furthermore, we discuss two particu...

We introduce a “generalized small inverse problem (GSIP)” and present an algorithm for solving this problem. GSIP is formulated as finding small solutions of f(x0, x1, . . . , xn) = x0h(x1, . . . , xn) + C = 0(mod M) for an n-variate polynomial h, non-zero integers C and M . Our algorithm is based on lattice-based Coppersmith technique. We provide a strategy for construction of a lattice basis ...

Motivated by important applications, the theory of mathematical programming has been extended to the case of infinitely many restrictions. At the same time, this theory knew remarcable developments since invexity and its further generalizations have been introduced as substitute of convexity. Here, we consider the multiobjective programming with a set of restrictions indexed in a compact. We ob...

The implementation results of an algorithm designed to solve semi-in&nite programming problems are reported. Due to its computational intensity, parallelisation is used in two stages of the algorithm—for evaluating the global optimum and for checking the feasibility of constraints. The algorithms are parallelised using MPI—the message passing interface. The algorithms are then applied to engine...