Strict lower semicontinuity of the level sets and invexity of a locally Lipschitz function

DOI10.1007/BF02192135zbMath0840.90119OpenAlexW1965291583MaRDI QIDQ1904692

Yanyan Li

Publication date: 1 February 1996

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02192135

zbMATH Keywords

Clarke generalized gradientinvexitylocally Lipschitz real-valued functionsstrict lower semicontinuity property

Mathematics Subject Classification ID

Nonlinear programming (90C30) Nonsmooth analysis (49J52)

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Cites Work

• Unnamed Item
• Unnamed Item
• On sufficiency of the Kuhn-Tucker conditions
• On functions whose stationary points are global minima
• On generalized pseudoconvex functions
• Note on generalized convex functions
• Nonsmooth invexity
• Lipschitzian properties of multifunctions
• Optimization and nonsmooth analysis
• What is invexity?
• Generalized invexity and duality theories with multifunctions
• On the notion of tangent cone in mathematical programming
• Generalized invexity for nonsmooth vector-valued mappings
• On locally Lipschitz vector-valued invex functions

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