On Approximating a Set-Valued Function Locally.

Abstract

Given a multi-valued mapping F, we address the problem of finding another multi-valued mapping H that agrees locally with F in some sense. We show that, contrary to the scalar case, introducing a derivative of F is hardly convenient. For the case when F is convex-compact-valued, we give some possible approximations, and at the same time we show their limitations. The present paper is limited to Informal demonstration of concepts and mechanisms. Formal statements and proofs will be published elsewhere. Keywords: convexity, multifunctions, differentiability, Newton scheme.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1985
Accession Number
ADA153540

Entities

People

  • C. Lemarechal
  • J. Zowe
  • V. F. Demyanov

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Classification
  • Continents
  • Contracts
  • Convex Sets
  • Demonstrations
  • Evolutionary Algorithms
  • Heuristic Methods
  • Inclusions
  • Mathematics
  • Military Research
  • North Carolina
  • Optimization
  • United States
  • Universities
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Operations Research
  • Systems Analysis and Design