Duality for multiobjective optimization via nonlinear Lagrangian functions

DOI10.1023/B:JOTA.0000012735.86699.a1zbMath1156.90436OpenAlexW2087732079MaRDI QIDQ1431703

Xiao Qi Yang, Xue Xiang Huang

Publication date: 11 June 2004

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

Full work available at URL: https://doi.org/10.1023/b:jota.0000012735.86699.a1

zbMATH Keywords

multiobjective optimizationstrong dualityasymptotic strong dualitynonlinear Lagrangians

Mathematics Subject Classification ID

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

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The proximal point method with a vectorial Bregman regularization in multiobjective DC programming ⋮ Pareto solutions as limits of collective traps: an inexact multiobjective proximal point algorithm ⋮ Inexact proximal point methods for multiobjective quasiconvex minimization on Hadamard manifolds ⋮ A scalarization proximal point method for quasiconvex multiobjective minimization ⋮ An interior proximal method in vector optimization ⋮ Duality for set-valued multiobjective optimization problems. I: Mathematical programming ⋮ Proximal point method for locally Lipschitz functions in multiobjective optimization of Hadamard manifolds ⋮ The Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization with Application to the Compromise Problem ⋮ A proximal point algorithm with quasi-distance in multi-objective optimization ⋮ Parallel proximal point methods for systems of vector optimization problems on Hadamard manifolds without convexity ⋮ A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems

Cites Work

• Theory of multiobjective optimization
• A Nonlinear Lagrangian Approach to Constrained Optimization Problems
• General lagrange-type functions in constrained global optimization Part I: auxiliary functions and optimality conditions
• Variational Analysis
• Nonlinear Lagrangian for Multiobjective Optimization and Applications to Duality and Exact Penalization
• Decreasing Functions with Applications to Penalization
• Extended Lagrange And Penalty Functions in Continuous Optimization^*
• Nonlinear Lagrangian theory for nonconvex optimization.
• Duality and exact penalization for vector optimization via augmented Lagrangian
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