Quadratic growth and critical point stability of semi-algebraic functions

Quadratic growth and critical point stability of semi-algebraic functions

We show that quadratic growth of a semi-algebraic function is equivalent to strong metric subregularity of the subdifferential—a kind of stability of generalized critical points. In contrast, this equivalence can easily fail outside of the semi-algebraic setting. As a consequence, we derive necessar...

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Veröffentlicht in:Mathematical programming 2015-11, Vol.153 (2), p.635-653
Hauptverfasser: Drusvyatskiy, D., Ioffe, A. D.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Calculus of Variations and Optimal Control
Optimization
Combinatorics
Critical point
Equivalence
Full Length Paper
Functions (mathematics)
Geometry
International relations-US
Mathematical analysis
Mathematical and Computational Physics
Mathematical functions
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Stability
Studies
Theoretical
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Beschreibung
Zusammenfassung:We show that quadratic growth of a semi-algebraic function is equivalent to strong metric subregularity of the subdifferential—a kind of stability of generalized critical points. In contrast, this equivalence can easily fail outside of the semi-algebraic setting. As a consequence, we derive necessary conditions and sufficient conditions for optimality in subdifferential terms.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-014-0820-y