Simplified optimality conditions for minimizing the difference of vector-valued functions

DOI10.1023/A:1017535424813zbMath0984.90053OpenAlexW1504778158MaRDI QIDQ5942220

Werner Oettli, Fabián Flores-Bazan

Publication date: 28 August 2001

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

Full work available at URL: https://doi.org/10.1023/a:1017535424813

zbMATH Keywords

conjugate functionsnonconvex minimization of a vector-valued functionphi-subdifferentials

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Optimality conditions and duality in mathematical programming (90C46)

Related Items (16)

Optimality conditions for the difference of convex set-valued mappings ⋮ Necessary optimality conditions for a set-valued fractional extremal programming problem under inclusion constraints ⋮ On the optimality conditions for D.C. vector optimization problems ⋮ Subdifferential and optimality conditions for the difference of set-valued mappings ⋮ A modified proximal point method for DC functions on Hadamard manifolds ⋮ The directional subdifferential of the difference of two convex functions ⋮ Conditions for the stability of ideal efficient solutions in parametric vector optimization via set-valued inclusions ⋮ Optimality conditions for vector optimization problems with difference of convex maps ⋮ Sufficient Optimality Conditions for a Bilevel Semivectorial D.C. Problem ⋮ On the subdifferentiability of the difference of two functions and local minimization ⋮ Optimality conditions for minimizing the difference of nonconvex vector-valued mappings ⋮ A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems ⋮ A difference-of-convex functions approach for sparse PDE optimal control problems with nonconvex costs ⋮ (\(\epsilon\)-)efficiency in difference vector optimization ⋮ Strict vector variational inequalities and strict Pareto efficiency in nonconvex vector optimization ⋮ Optimality conditions for D.C. vector optimization problems under reverse convex constraints

Cites Work

• A duality principle for non-convex optimisation and the calculus of variations
• Conjugate functions for convex and nonconvex duality
• On minima of the difference of functions
• Kolmogorov conditions for vectorial optimization problems
• Sandwich Theorems for Semicontinuous Operators
• A formula on the approximate subdifferential of the difference of convex functions
• On $\Phi $-Convexity in Extremal Problems
• A Fenchel-Rockafellar type duality theorem for maximization
• MINKOWSKI DUALITY AND ITS APPLICATIONS
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