Balance set and Pareto solutions in linear space with application to ongoing optimal resource allocation, investment planning, production, and control problems with multiple objectives

DOI10.1016/j.mcm.2003.09.033zbMath1112.90076OpenAlexW1977248891MaRDI QIDQ1764960

Efim A. Galperin

Publication date: 22 February 2005

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mcm.2003.09.033

zbMATH Keywords

MCDMPareto solutionsBalance set

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Management decision making, including multiple objectives (90B50) Programming in abstract spaces (90C48) Resource and cost allocation (including fair division, apportionment, etc.) (91B32)

Related Items (3)

The Isaacs equation for differential games, totally optimal fields of trajectories and related problems ⋮ Non-causal models in long term planning via set contractive optimal control methods ⋮ Information transmittal, time uncertainty and special relativity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Set contraction algorithm for computing Pareto set in nonconvex nonsmooth multiobjective optimization
• Goal-optimal Pareto solution of multiobjective linear programs and its computing with standard single objective LP software
• Nonscalarized multiobjective global optimization
• A saddle-point characterization of Pareto optima
• Pareto analysis vis-à-vis balance space approach in multiobjective global optimization
• Equivalence of balance points and Pareto solutions in multiple-objective programming
• Convergence estimates for crude approximations of a Pareto set.
• The balance space approach in optimization with Riesz spaces valued objectives. An application to financial markets.
• Min-max formulation of the balance number in multiobjective global optimization.
• The balance space approach to multicriteria decision making -- involving the decision maker.
• Norm-based approximation in multicriteria programming.
• Balance space in airport construction: Application to the North Sea island option for Schiphol Airport
• A characterization of weakly efficient points
• Duality theory and slackness conditions in multiobjective linear programming
• Retrieval and use of the balance set in multiobjective global optimization
• Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
• Use of \(P_ \tau\)-nets for the approximation of the Edgeworth-Pareto set in multicriteria optimization
• Necessary and Sufficient Conditions for a Pareto Optimum in Convex Programming
• Finding all efficient extreme points for multiple objective linear programs
• Duality of nonscalarized multiobjective linear programs: dual balance, level sets, and dual clusters of optimal vectors.

This page was built for publication: Balance set and Pareto solutions in linear space with application to ongoing optimal resource allocation, investment planning, production, and control problems with multiple objectives