
Accession Number : ADA138202
Title : Convexity and Concavity Properties of the Optimal Value Function in Parametric Nonlinear Programming.
Descriptive Note : Scientific rept.,
Corporate Author : GEORGE WASHINGTON UNIV WASHINGTON DC INST FOR MANAGEMENT SCIENCE AND ENGINEERING
Personal Author(s) : Fiacco,A V ; Kyparisis,J
PDF Url : ADA138202
Report Date : 21 Dec 1982
Pagination or Media Count : 63
Abstract : Convexity and concavity properties of the optimal value function f* are considered for the general parametric optimization problem P (E) of the form min f(x,E) s.t. x E R(E). Such properties of f* and the solution set map S* form an important part of the theoretical basis for sensitivity, stability, and parametric analysis in mathematical optimization. Sufficient conditions are given for several standard types of convexity and concavity of f*, in terms of respective convexity and concavity assumptions on f and the feasible region pointtoset map R. Specializations of these results to the general parametric inequalityequality constrained nonlinear programming problem and its righthandside version are provided. Convexity properties of the solution pointtoset map S* for the general problem P(E) are also briefly considered. Although most of the results appear to be new, some basic results were obtained previously in a somewhat different setting. These are included here and related to the new developments, thus providing the first comprehensive survey of these important characterizations. (Author)
Descriptors : *Nonlinear programming, *Parametric programming, Optimization
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE