Optimality conditions for nonsmooth multiobjective optimization using Hadamard directional derivatives

DOI10.1007/s10957-007-9169-1zbMath1149.90134OpenAlexW1981928753MaRDI QIDQ946309

Phan Quoc Khanh, Nguyen Dinh Tuan

Publication date: 23 September 2008

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

Full work available at URL: https://doi.org/10.1007/s10957-007-9169-1

zbMATH Keywords

Hadamard directional derivativesMultiobjective optimizationFirm efficiencyWeak efficiency

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Optimality conditions and duality in mathematical programming (90C46) Nonsmooth analysis (49J52)

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Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Second-order conditions for efficiency in nonsmooth multiobjective optimization problems
• First and second order optimality conditions using approximations for nonsmooth vector optimization in Banach spaces
• From scalar to vector optimization.
• First and second order sufficient conditions for strict minimality in nonsmooth vector optimization.
• Second order optimality conditions for the extremal problem under inclusion constraints
• Optimality conditions for \(C^{1,1}\) constrained multiobjective problems
• Directional Kuhn--Tucker condition and duality for quasidifferentiable programs
• Weakly upper Lipschitz multifunctions and applications in parametric optimization
• Necessary conditions in nonsmooth minimization via lower and upper subgradients
• Second-order necessary conditions for optimality in nonsmooth nonlinear programming
• Second-order conditions in \(C^{1,1}\) constrained vector optimization
• On Second-Order Subdifferentials and Their Applications
• Stability in Mathematical Programming with Nondifferentiable Data
• Calculus of Dini subdifferentials of functions and contingent coderivatives of set-valued maps
• Differentiability of Relations and Differential Stability of Perturbed Optimization Problems
• Second‐Order Optimality Conditions for Scalar and Vector Optimization Problems in Banach Spaces
• Necessary and Sufficient Conditions for Isolated Local Minima of Nonsmooth Functions
• Some continuity properties of polyhedral multifunctions
• Second-order necessary and sufficient conditions in multiobjective programming^∗
• Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces
• Approximate Jacobian Matrices for Nonsmooth Continuous Maps and C¹-Optimization
• Second-Order Conditions for Optimization Problems with Constraints
• Approximate Hessian matrices and second-order optimality conditions for nonlinear programming problems with C¹-data
• Second order approximations and dual necessary optimality conditions
• Variational Analysis
• Tilt Stability of a Local Minimum
• Approximation of set-valued functions by single-valued one
• An Extended Extremal Principle with Applications to Multiobjective Optimization
• Metric regularity and subdifferential calculus
• Equilibrium problems with equilibrium constraints via multiobjective optimization
• Variational Analysis and Generalized Differentiation I
• A Multiplier Rule for Multiobjective Programming Problems with Continuous Data
• Constrained Minima and Lipschitzian Penalties in Metric Spaces
• Stability of Locally Optimal Solutions
• Approximations and Metric Regularity in Mathematical Programming in Banach Space
• Optimality conditions for \(C^{1,1}\) vector optimization problems
• Strict efficiency in vector optimization