Abstract
We now return to the general theory of extremal problems, and try to determine whether the necessary conditions for a minimum developed in Lecture 6 are also sufficient. Of course, elementary examples show that in general this is not true. Nevertheless, we shall prove that, under certain additional assumptions, the necessary extremum conditions are also sufficient, in an important class of extremal problems — convex problems. Sufficient conditions for non-convex problems can probably be formulated in terms of the second variation. However, results in this field are as yet quite sporadic, and we shall not dwell on them here.
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© 1972 Springer-Verlag Berlin · Heidelberg
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Girsanov, I.V., Poljak, B.T. (1972). Sufficient Extremum Conditions. In: Poljak, B.T. (eds) Lectures on Mathematical Theory of Extremum Problems. Lecture Notes in Economics and Mathematical Systems, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80684-1_16
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DOI: https://doi.org/10.1007/978-3-642-80684-1_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-05857-1
Online ISBN: 978-3-642-80684-1
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