Second-order Variational Analysis and Characterizations of Tilt-stable Optimal Solutions in Finite and Infinite Dimensions1
نویسندگان
چکیده
The paper is devoted to developing second-order tools of variational analysis and their applications to characterizing tilt-stable local minimizers of constrained optimization problems in finite-dimensional and infinite-dimensional spaces. The importance of tilt stability has been well recognized from both theoretical and numerical aspects of optimization. Based on second-order generalized differentiation, we obtain qualitative and quantitative characterizations of tilt stability in general frameworks of constrained optimization and establish its relationships with strong metric regularity of subgradient mappings and uniform second-order growth. The results obtained are applied to deriving new necessary and sufficient conditions for tilt-stable minimizers in problems of nonlinear programming with twice continuously differentiable data in Hilbert and Euclidean spaces.
منابع مشابه
Second-order characterizations of tilt stability with applications to nonlinear programming
The paper is devoted to the study of tilt-stable local minimizers of general optimization problems in finite-dimensional spaces and its applications to classical nonlinear programs with twice continuously differentiable data. The importance of tilt stability has been well recognized from both theoretical and numerical aspects of optimization, and this notion has been extensively studied in the ...
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