Convexity and Concavity Properties of the Optimal Value Function in Parametric Nonlinear Programming.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 21, 1982
- Accession Number
- ADA138202
Entities
People
- A. V. Fiacco
- J. Kyparisis
Organizations
- George Washington University