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Necessary and sufficient conditions for differentiable nonscalar-valued functions to attain extrema

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2 Author(s)
Athans, M. ; Massachusetts Institute of Technology, Cambridge, MA, USA ; Geering, H.

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.

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Automatic Control, IEEE Transactions on  (Volume:18 ,  Issue: 2 )