Title :
Necessary and sufficient conditions for differentiable nonscalar-valued functions to attain extrema
Author :
Athans, Michael ; Geering, Hans P.
Author_Institution :
Massachusetts Institute of Technology, Cambridge, MA, USA
fDate :
4/1/1973 12:00:00 AM
Abstract :
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 is reported. The applicability of the theory to the analysis of linear least squares vector estimation problem is demonstrated.
Keywords :
Least-squares estimation; Optimization methods; Calculus; Constraint theory; Control theory; Cost function; Least squares approximation; Mathematical programming; Optimal control; Sufficient conditions; Variable speed drives; Vectors;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.1973.1100249
