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ON SOME TOPICS IN SEMI-INFINITE PROGRAMMING (A PRELIMINARY DISCUSSION)
 

Summary: ON SOME TOPICS IN SEMI-INFINITE PROGRAMMING
(A PRELIMINARY DISCUSSION)
November 23, 2005
GEORG STILL
ABSTRACT. A semi-infinite programming problem is an optimization problem in
which finitely many variables appear in infinitely many constraints. This model natu-
rally arises in an abundant number of applications in different fields of mathematics,
economics and engineering. The present paper intends to give a short introduction
into the field and to present some preliminary discussion on the complexity of linear
SIP.
1. INTRODUCTION
1.1. Problem formulation. A semi-infinite program (SIP) is an optimization problem
in finitely many variables x = .x1;:::; xn/ Rn
on a feasible set described by infinitely
many constraints:
(1) P: min
x
f .x/ s.t. g.x; y/ 0 y Y ;
where Y is an infinite index set. F will denote the feasible set, v = inf{ f .x/ | x F }
the optimal value and S = {x F | f .x/ = v} the set of minimizers of the problem.

  

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente

 

Collections: Engineering