Stable Operators in Analysis and OptimizationThe main purpose of this book is to provide an advanced account of some aspects of differentiable stable operators in Banach and Hilbert spaces. The theory of linear and nonlinear stable operators is presented in a systematic way and possible applications are described. The book is useful to graduate students and researchers. |
Contents
Stability Concept | 1 |
Stable Operators and WellPosedness | 31 |
Generalization to Nonlinear Problems | 67 |
Copyright | |
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A(xo Assume assumptions of Theorem B(h₁ bounded called compact concept consider continuous function continuously Fréchet differentiable convergence convex function convex set convex subset corresponding defined Definition denote differentiable at xo discretization method element formulate Fréchet derivative Fréchet differentiable operator Gâteaux derivative H₁ ill-posed inequality Lemma linear continuous operators linear operator linear problem Lipschitz continuous lower semicontinuous lower semicontinuous functional Mapping Theorem metric space minimum norm solution monotone operator Moreover neighborhood nonempty normed space Open Mapping Theorem open set operator A'(x optimal control optimal control problem optimization problem optimization theory Proof proper convex quasi-solution real Banach spaces real Hilbert space regularity conditions satisfying sequence solvability space and let stabilizing function star expanding strongly convex strongly stable operators subspace surjective symmetric operator Theorem 16 Theorem 33 Tikhonov well-posedness tion topological space unique solution vector space W₁ weak topology xº¹¹ xopt Y₁