‎Linear semi-infinite programming problem is an important class of optimization problems which deals with infinite constraints‎. ‎In this paper‎, ‎to solve this problem‎, ‎we combine a discretization method and a neural network method‎. ‎By a simple discretization of the infinite constraints,we convert the linear semi-infinite programming problem into linear programming problem‎. ‎Then‎, ‎we use...

The purpose of this paper is to consider a class of nonsmooth minimax fractional semi-infinite programming problem. Based on the concept of H − tangent derivative, a new generalization of convexity, namely generalized uniform ( , ) H B ρ − invexity, is defined for this problem. For such semi-infinite programming problem, several sufficient optimality conditions are established and proved by uti...

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...

where is a (possibly infinite) set, f : R ! R is an extended real valued function and g : R ! R. In the above formulation, a feasible point x 2 R is supposed to satisfy the constraints gðx,!Þ 0 for all !2 , and no structural assumptions are made about the set . In some situations it is natural to require that these constraints hold for almost every (a.e.) !2 . That is, the set is equipped with ...

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...

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...

The Remez penalty and smoothing algorithm (RPSALG) is a unified framework for penalty and smoothing methods for solving min-max convex semiinfinite programing problems, whose convergence was analyzed in a previous paper of three of the authors. In this paper we consider a partial implementation of RPSALG for solving ordinary convex semi-infinite programming problems. Each iteration of RPSALG in...