Abstract
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 infinite-dimensional spaces with many results new also in finite-dimensional settings. 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 spaces.
| Original language | English |
|---|---|
| Pages (from-to) | 159-180 |
| Number of pages | 22 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 86 |
| DOIs | |
| State | Published - 2013 |
Bibliographical note
Funding Information:This research was supported by the National Science Foundation under grant DMS-1007132 .
Funding Information:
The research of the first author was partly supported by the Australian Research Council under grant DP-12092508 and by the Portuguese Foundation of Science and Technologies under grant MAT/11109 .
Keywords
- First-order and second-order generalized differentiation
- Lipschitzian stability
- Second-order growth
- Strong metric regularity
- Variational analysis and optimization
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
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