期刊
SIAM JOURNAL ON OPTIMIZATION
卷 22, 期 4, 页码 1655-1684出版社
SIAM PUBLICATIONS
DOI: 10.1137/120864660
关键词
variational analysis; metric subregularity; generalized differentiation; error bounds; proximal point method
资金
- Australian Research Council [DP-12092508]
- USA National Science Foundation [DMS-1007132]
- European Regional Development Fund (FEDER)
- Foundation for Science and Technology
- Operational Program for Competitiveness Factors
- Strategic Reference Framework [PTDC/MAT/111809/2009]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1007132] Funding Source: National Science Foundation
This paper is mainly devoted to the study and applications of Holder metric subregularity (or metric q-subregularity of order q is an element of (0, 1]) for general set-valued mappings between infinite-dimensional spaces. Employing advanced techniques of variational analysis and generalized differentiation, we derive neighborhood and point-based sufficient conditions as well as necessary conditions for q-metric subregularity with evaluating the exact subregularity bound, which are new even for the conventional (first-order) metric subregularity in both finite and infinite dimensions. In this way we also obtain new fractional error bound results for composite polynomial systems with explicit calculating fractional exponents. Finally, metric q-subregularity is applied to conduct a quantitative convergence analysis of the classical proximal point method (PPM) for finding zeros of maximal monotone operators on Hilbert spaces.
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