Journal Article10.1007/BF00934096
Infinitely constrained optimization problems
188
TL;DR: In this article, a generalized cutting-plane algorithm designed to solve problems of the form min{f(x) :x ∈ X andg(x,y) ∈ 0 for ally ∈ Y} is described.
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Abstract: A generalized cutting-plane algorithm designed to solve problems of the form min{f(x) :x ∈X andg(x,y) ∈ 0 for ally ∈Y} is described. Convergence is established in the general case (f,g continuous,X andY compact). Constraint dropping is allowed in a special case [f,g(·,y) convex functions,X a convex set]. Applications are made to a variety of max-min problems. Computational considerations are discussed.
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Numerical treatment of a class of semi-infinite programming problems
TL;DR: The aim of this paper is to describe methods of handling problems of handling optimization problems numerically in an effective manner and indicate a number of applications.
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Cutting-plane methods without nested constraint sets
TL;DR: General conditions for the convergence of a class of cutting-plane algorithms without requiring that the constraint sets for the sub-problems be sequentially nested are given.
53