Titlebook: Lectures on Mathematical Theory of Extremum Problems; Igor Vladimirovich Girsanov,B. T. Poljak Book 1972 Springer-Verlag Berlin · Heidelbe

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Topological Linear Spaces, Convex Sets, Weak Topologies,We shall assume that the space in which the extremal problem is to be solved is a topological linear space. We briefly recall the relevant concepts.

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Hahn-Banach Theorem,We shall now discuss the Hahn-Banach Theorem, which is the basic tool in the subsequent analysis. We shall not present proofs of the theorems, since they can be found in the extensive literature on functional analysis.

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Necessary Extremum Conditions (Euler-Lagrange Equation),We have now prepared sufficient auxiliary material to enable us to proceed to analysis of extremum problems.

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Feasible Directions,We shall now describe how to determine the feasible directions. Throughout this lecture, K . at a point x. for a set Q in a topological linear space.

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