We consider the class of linear programs with infinitely many variables and constraints having the property that every constraint contains at most finitely many variables while every variable appears in at most finitely many constraints. Examples include production planning and equipment replacement over an infinite horizon. We form the natural dual linear programming problem and prove strong d...

Fourier-Motzkin elimination is a projection algorithm for solving finite linear programs. Weextend Fourier-Motzkin elimination to semi-infinite linear programs which are linear programswith finitely many variables and infinitely many constraints. Applying projection leads to newcharacterizations of important properties for primal-dual pairs of semi-infinite programs suchas zero ...

We consider semi-infinite linear programs with countably many constraints indexed by the natural numbers. When the constraint space is the vector space of all real valued sequences, we show that the finite support (Haar) dual is equivalent to the algebraic Lagrangian dual of the linear program. This settles a question left open by Anderson and Nash [2]. This result implies that if there is a du...

In this paper, we propose an explicit exchange algorithm for solving semiinfinite programming problem (SIP) with second-order cone (SOC) constraints. We prove, by using the slackness complementarity conditions, that the algorithm terminates in a finite number of iterations and the obtained solution sufficiently approximates the original SIP solution. In existing studies on SIPs, only the nonneg...

The paper studies the connections and differences between bilevel problems (BL) and generalized semi-infinite problems (GSIP). Under natural assumptions (GSIP) can be seen as a special case of a (BL). We consider the so-called reduction approach for (BL) and (GSIP) leading to optimality conditions and Newtontype methods for solving the problems. We show by a structural analysis that for (GSIP)-...

We consider the class of linear programs that can be formulated with infinitely many variables and constraints but where each constraint has only finitely many variables. This class includes virtually all infinite horizon planning problems modeled as infinite stage linear programs. Examples include infinite horizon production planning under time-varying demands and equipment replacement under t...

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...

We present a primal method for the solution of the semi-infinite linear programming problem with constraint index set S. We begin with a detailed treatment of the case when S is a closed line interval in ~. A characterization of the extreme points of the feasible set is given, together with a purification algorithm which constructs an extreme point from any initial feasible solution. The set of...

This paper presents an overview of the research progress in deterministic global optimization during the last decade (1998–2008). It covers the areas of twice continuously differentiable nonlinear optimization, mixed-integer nonlinear optimization, optimization with differential-algebraic models, semi-infinite programming, optimization with grey box/nonfactorable models, and bilevel nonlinear o...