| A Question about Nonlinear Functional |
| Received:February 27, 1989 |
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| Abstract: |
| Suppose that H is a Hilbert space, D is a convex closed set inis a functioal, f(x)=1/2‖x‖2-g(x). Suppose that the minimum of f(x) withrespect to D is attained at x0∈D and f(x) has a bounded linear Gateaux differential at x0. In this paper we prove that f(x0) is a critical value of f(x) when and only when g′(x0)∈ID(x0)={(1-λ)x0 λy|y∈D.λ≥0}. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.1990.04.020 |
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