Accession Number : AD0738311

Title :   Necessary and Sufficient Conditions for Differentiable Non-Scalar-Valued Functions to Attain Extrema,

Corporate Author : MASSACHUSETTS INST OF TECH CAMBRIDGE ELECTRONIC SYSTEMS LAB

Personal Author(s) : Geering,Hans P. ; Athans,Michael

Report Date : JAN 1972

Pagination or Media Count : 30

Abstract : The paper reports a self-contained theory of extrema (viz. suprema, maxima, minima, and infima) of differentiable functions of several (possibly infinitely many) variables mapping into finite-dimensional integrally closed directed partially ordered linear spaces. The applicability of the theory to the analysis of linear least-squares vector estimation problems is demonstrated. (Author)

Descriptors :   (*ADAPTIVE CONTROL SYSTEMS, MATHEMATICAL MODELS), (*FUNCTIONS(MATHEMATICS), OPTIMIZATION), FUNCTIONAL ANALYSIS, MATHEMATICAL PROGRAMMING, ALGEBRAIC TOPOLOGY, VECTOR SPACES, MAPPING(TRANSFORMATIONS), STOCHASTIC PROCESSES, DIFFERENTIAL EQUATIONS, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE