Sigma-subdifferential and its application to minimization problem

Sigma-subdifferential and its application to minimization problem

In this paper, we study σ -subdifferentials of σ -convex functions. Two equivalent conditions for σ -convexity are given. The formula for the σ -subdifferential of a sum of two functions is established. In terms of σ -subdifferential and Clarke’s normal cone, some Fermat’s rules for minimization pro...

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Veröffentlicht in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2020-07, Vol.24 (3), p.539-551
Hauptverfasser: Huang, Hui, Sun, Chunyou
Format: Artikel
Sprache:eng
Schlagworte:
Calculus of Variations and Optimal Control
Optimization
Convexity
Differential equations
Econometrics
Fourier Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Optimization
Potential Theory
Topological manifolds
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Zusammenfassung:In this paper, we study σ -subdifferentials of σ -convex functions. Two equivalent conditions for σ -convexity are given. The formula for the σ -subdifferential of a sum of two functions is established. In terms of σ -subdifferential and Clarke’s normal cone, some Fermat’s rules for minimization problems are obtained.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-019-00693-1