Second-order conditions for efficiency in nonsmooth multiobjective optimization problems

DOI10.1023/B:JOTA.0000042594.46637.b4zbMath1082.90106MaRDI QIDQ819338

N. E. Zubov

Publication date: 28 March 2006

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

zbMATH Keywords

efficient solutionssecond-order constraint qualificationssecond-order tangent setssecond-order directional derivatives\(C^{1+}\) functionsmultiobjective minimization problems

Mathematics Subject Classification ID

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

Related Items (16)

A note on second-order Karush–Kuhn–Tucker necessary optimality conditions for smooth vector optimization problems ⋮ Locally Lipschitz vector optimization problems: second-order constraint qualifications, regularity condition and KKT necessary optimality conditions ⋮ Second-order strong Karush/Kuhn-Tucker conditions for proper efficiencies in multiobjective optimization ⋮ New second-order Karush-Kuhn-Tucker optimality conditions for vector optimization ⋮ On Constraint Qualifications for Multiobjective Optimization Problems with Vanishing Constraints ⋮ Bounded sets of KKT multipliers in vector optimization ⋮ Second-order optimality conditions in minimax optimization problems ⋮ A noninterior path following algorithm for solving a class of multiobjective programming problems ⋮ Proper efficiency and proper Karush-Kuhn-Tucker conditions for smooth multiobjective optimization problems ⋮ Homotopy method for a general multiobjective programming problem ⋮ Second-order optimality conditions for vector problems with continuously Fréchet differentiable data and second-order constraint qualifications ⋮ Optimality conditions for nonsmooth multiobjective optimization using Hadamard directional derivatives ⋮ Second-order necessary conditions in locally Lipschitz optimization with inequality constraints ⋮ Strong second-order Karush–Kuhn–Tucker optimality conditions for vector optimization ⋮ Second-order optimality conditions and Lagrange multiplier characterizations of the solution set in quasiconvex programming ⋮ Unnamed Item

Cites Work

• Generalized Hessian matrix and second-order optimality conditions for problems with \(C^{1,1}\) data
• Efficiency and proper efficiency in vector maximization with respect to cones
• Second-order necessary conditions of the Kuhn-Tucker type under new constraint qualifications
• Constrained qualifications in multiobjective optimization problems: Differentiable case
• On the cones of tangents with applications to mathematical programming
• A necessary second-order optimality condition in nonsmooth mathematical programming
• A Generalized Second-Order Derivative in Nonsmooth Optimization
• Optimization and nonsmooth analysis
• A unified theory of first and second order conditions for extremum problems in topological vector spaces
• On second-order directional derivatives
• Generalized Kuhn–Tucker Conditions for Mathematical Programming Problems in a Banach Space
• Convex Analysis

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