Approximating the nondominated set of an MOLP by approximately solving its dual problem

DOI10.1007/s00186-007-0194-5zbMath1184.90161OpenAlexW2030295088MaRDI QIDQ999127

Lizhen Shao, Matthias Ehrgott

Publication date: 30 January 2009

Published in: Mathematical Methods of Operations Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00186-007-0194-5

zbMATH Keywords

Multiobjective linear programming\(\epsilon \)-nondominated setGeometric dualityRadiotheraphy treatment planning

Mathematics Subject Classification ID

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

Related Items (16)

Geometric Duality Results and Approximation Algorithms for Convex Vector Optimization Problems ⋮ A Benson-type algorithm for bounded convex vector optimization problems with vertex selection ⋮ A revised Pascoletti-Serafini scalarization method for multiobjective optimization problems ⋮ A Benson type algorithm for nonconvex multiobjective programming problems ⋮ A dual variant of Benson's ``outer approximation algorithm for multiple objective linear programming ⋮ Primal and dual approximation algorithms for convex vector optimization problems ⋮ Reducing wall-clock time for the computation of all efficient extreme points in multiple objective linear programming ⋮ Mathematical optimization in intensity modulated radiation therapy ⋮ Mathematical optimization in intensity modulated radiation therapy ⋮ An algorithm to solve polyhedral convex set optimization problems ⋮ A parametric simplex algorithm for linear vector optimization problems ⋮ Primal and dual multi-objective linear programming algorithms for linear multiplicative programmes ⋮ Benson type algorithms for linear vector optimization and applications ⋮ Scalarization for characterization of approximate strong/weak/proper efficiency in multi-objective optimization ⋮ Optimality conditions via a unified direction approach for (approximate) efficiency in multiobjective optimization ⋮ Optimality conditions via scalarization for approximate quasi efficiency in multiobjective optimization

Cites Work

• A dual variant of Benson's ``outer approximation algorithm for multiple objective linear programming
• Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning
• On-line and off-line vertex enumeration by adjacency lists
• Hybrid approach for solving multiple-objective linear programs in outcome space
• An outer approximation algorithm for generating all efficient extreme points in the outcome set of a multiple objective linear programming problem
• Approximation methods in multiobjective programming
• State Constraints in Convex Control Problems of Bolza
• Unnamed Item
• Unnamed Item

This page was built for publication: Approximating the nondominated set of an MOLP by approximately solving its dual problem