 
Summary: ON SOME TOPICS IN SEMIINFINITE PROGRAMMING
(A PRELIMINARY DISCUSSION)
November 23, 2005
GEORG STILL
ABSTRACT. A semiinfinite 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 semiinfinite 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.
