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 point-to-set map R. Specializations of these results to the general parametric inequality-equality constrained nonlinear programming problem and its right-hand-side version are provided. Convexity properties of the solution point-to-set 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