Abstract
This article presents a systematic study of partial second-order subdifferentials for extended-real-valued functions, which have already been applied to important issues of variational analysis and constrained optimization in finite-dimensional spaces. The main results concern developing extended calculus rules for these second-order constructions in both finite-dimensional and infinite-dimensional frameworks. We also provide new applications of partial second-order subdifferentials to Lipschitzian stability of stationary point mappings in parametric constrained optimization and discuss some other applications.
| Original language | English |
|---|---|
| Pages (from-to) | 1113-1151 |
| Number of pages | 39 |
| Journal | Numerical Functional Analysis and Optimization |
| Volume | 35 |
| Issue number | 7-9 |
| DOIs | |
| State | Published - 3 Jul 2014 |
Bibliographical note
Funding Information:Research of N. M. Nam was partly supported by the Simons Foundation under grant #208785.
Funding Information:
Research of B. S. Mordukhovich was partly supported by the National Science Foundation under grant DMS-1007132, by the Australian Research Council under grant DP-12092508, and by the Portuguese Foundation of Science and Technologies under grant MAT/11109.
Keywords
- Coderivatives
- Generalized differentiation
- Parametric constrained optimization
- Second-order subdifferentials
- Stability
- Stationary point mappings
- Variational analysis
ASJC Scopus subject areas
- Analysis
- Signal Processing
- Computer Science Applications
- Control and Optimization
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