Super efficiency in vector optimization with nearly convexlike set-valued maps.

DOI10.1016/S0022-247X(02)00452-3zbMath1106.90375MaRDI QIDQ1857012

Aparna Mehra

Publication date: 11 February 2003

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Set-valued mapSuper efficiencyNearly convexlike mapSuper dualitySuper saddle point

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Optimality conditions and duality in mathematical programming (90C46)

Related Items (15)

A kind of unified super efficiency via assumption (A) and applications in vector optimization ⋮ Proximal Proper Saddle Points in Set-Valued Optimization ⋮ Strict efficiency in vector optimization with nearly convexlike set-valued maps ⋮ Tightly proper efficiency in vector optimization with nearly cone-subconvexlike set-valued maps ⋮ Connectedness of Henig weakly efficient solution set for set-valued optimization problems ⋮ \(E\)-super efficiency of set-valued optimization problems involving improvement sets ⋮ Superefficiency in vector optimization with nearly subconvexlike set-valued maps ⋮ Strong duality with super efficiency in set-valued optimization ⋮ The Lagrange multiplier rule for super efficiency in vector optimization ⋮ Optimality conditions for Henig and globally proper efficient solutions with ordering cone has empty interior ⋮ Hartley proper efficiency in multiobjective optimization problems with locally Lipschitz set-valued objectives and constraints ⋮ Higher-order variational sets and higher-order optimality conditions for proper efficiency in set-valued nonsmooth vector optimization ⋮ Scalarization and saddle points of approximate proper solutions in nearly subconvexlike vector optimization problems ⋮ Henig efficiency in vector optimization with nearly cone-subconvexlike set-valued functions ⋮ Characterizations of Hartley proper efficiency in nonconvex vector optimization

Cites Work

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• Existence and Lagrangian duality for maximization of set-valued functions
• An improved definition of proper efficiency for vector maximization with respect to cones
• Benson proper efficiency in the vector optimization of set-valued maps
• Characterizations of super efficiency in cone-convexlike vector optimization with set-valued maps
• Optimization of set-valued functions
• Lagrangian multipliers, saddle points, and duality in vector optimization of set-valued maps
• Lagrangian duality for minimization of nonconvex multifunctions
• Proper efficiency and the theory of vector maximization
• Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
• Proper Efficient Points for Maximizations with Respect to Cones
• Super Efficiency in Vector Optimization
• Super efficiency in convex vector optimization
• Optimality conditions for maximizations of set-valued functions

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