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Home  >  Transasctions of NAMP VOL3

8. Optimization of Convex Functions in Infinite Dimensional Spaces by Eze E.O. and Obasi U.E. Transactions of NAMP Vol 3, (Jan, 2017), pp 39 – 44
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Abstract

This paper considered the optimization of convex functions in infinite dimensional spaces. Requisite theorems were reviewed and concise proofs of the relevant results given. Some analogues of Bolzano-Weirestrass results in infinite dimensional spaces were studied using the Eberlein-Smul’yan theorem. The main thrust is on the application of Lax-Milgram theorem which guarantees the existence of a unique minimizer of a convex functional defined on the Sobolev spacesH_0^1 (Ω). Finally example was given to illustrate the results. The main contribution is that every finite dimensional space problem has an analoguous infinite dimensional space version provided the right topology and assumptions are made.

Keywords: Convex Functions, Eberlein-Smul’yan Theorem, Lax-Milgram Theorem, Sobolev Spaces, Infinite Dimensional Spaces

Mathematics subject classification: 34A05, 33E05, 34C29.


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