Regularized minimization under weaker hypotheses |
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Authors: | Alain Gioan |
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Institution: | (1) Département de Mathématiques, Université de Nice, I. M. S. P., Parc Valrose, 06034 Nice Cedex, France |
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Abstract: | LetV andW be two Banach spaces, withV reflexive, a bounded convex set ofV, A a linear mapping fromV intoW, and letF be a convex functional onW. We minimizeJ(v)=F(Av) on using hypotheses about particular sequences in IfV is uniformly convex, we prove existence and uniqueness of a solution of minimal norm minimizingJ. In the Hilbert space case, withF defined byF(w)=w–f
2,f given inW, we get existence and uniqueness of the projection off on A(), which generalizes the case where A() is a closed set ofW (taking closed andA continuous). Finally, we give examples, and we study an unbounded operator case. |
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