Quasimonotone Multifunctions; Applications to Optimality Conditions in Quasiconvex Programming

DOI10.1080/01630569208816477zbMath0758.49010OpenAlexW2083708931MaRDI QIDQ4029142

Abdelhak Hassouni

Publication date: 7 March 1993

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630569208816477

zbMATH Keywords

normal conequasiconvexityoptimality conditionslevel setlocally Lipschitz functionsgeneralized gradientsquasimonotonicity for multifunctions

Mathematics Subject Classification ID

Variational inequalities (49J40) Nonsmooth analysis (49J52) Set-valued functions (26E25) Programming in abstract spaces (90C48) Convexity of real functions of several variables, generalizations (26B25)

Related Items (10)

Lipschitz B-vex functions and nonsmooth programming ⋮ Generalized monotonicity of a separable product of operators: The multivalued case ⋮ Generalized monotonicity of subdifferentials and generalized convexity ⋮ Generalized convexity of functions and generalized monotonicity of set-valued maps ⋮ A survey of recent[1985-1995advances in generalized convexity with applications to duality theory and optimality conditions] ⋮ Algorithm for the generalized Φ-strongly monotone mappings and application to the generalized convex optimization problem ⋮ A sufficient optimality theoriem for protoconvex programs ⋮ Quasi-convex functions and applications to optimality conditions in nonlinear programming ⋮ Characterization of nonsmooth functions through their generalized gradients ⋮ Optimality conditions for non-lipschitz generalized convex programming via clarke-rockafellar gradients

Cites Work

• Generalized gradients of Lipschitz functionals
• Nine kinds of quasiconcavity and concavity
• Seven kinds of monotone maps
• Continuity properties of the normal cone to the level sets of a quasiconvex function
• Weak lower subdifferentials and applications
• Some properties of nondifferentiable pseudoconvex functions
• Characterization of nonsmooth functions through their generalized gradients
• A First Order Sufficient Condition for Optimality in Nonsmooth Optimization
• On the anti-monotonicity of differential mappings connected with general equilibrium problem
• Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces
• Convex Analysis

This page was built for publication: Quasimonotone Multifunctions; Applications to Optimality Conditions in Quasiconvex Programming