SOME PROPERTIES OF AN OPTIMAL VALUE FUNCTION.
Abstract
If f(. . .) denotes a functional; BxM -- E(1) (B = real normed linear space, M = metric space), and if f(superscript o)(.) denotes an associated (optimal value) functional defined by the rule f(superscript o)(x) = sup f (x, mu) and the point mu belongs to the set M then the following questions arise: (1) Where is f(superscript o) continuous; (2) Where is f(superscript o) differentiable. Within the framework of certain reasonable assumptions on the properties of M and f, this paper answers questions 1 and 2. In particular, it offers a necessary and sufficient condition for the existence of a continuous derivative of f(superscript o) on subsets of B.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1966
- Accession Number
- AD0481551
Entities
People
- Joseph C. Dunn
Organizations
- Grumman