A coradiant based scalarization to characterize approximate solutions of vector optimization problems with variable ordering structures

This paper investigates some properties of approximate efficiency in variable ordering structures where the variable ordering structure is given by a special set valued map. We characterize e -minimal and e - nondominated elements as approximate solutions of a multiobjective optimization problem with a variable ordering structure and give necessary and sufficient conditions for these solutions, via scalarization.

[1]  Refail Kasimbeyli,et al.  Multiobjective Programming and Multiattribute Utility Functions in Portfolio Optimization , 2009, INFOR Inf. Syst. Oper. Res..

[2]  中嶋 博 Convex Programming の新しい方法 (開学記念号) , 1966 .

[3]  Behnam Soleimani,et al.  Characterization of Approximate Solutions of Vector Optimization Problems with a Variable Order Structure , 2014, J. Optim. Theory Appl..

[4]  Gabriele Eichfelder,et al.  Variable Ordering Structures in Vector Optimization , 2014, Vector Optimization.

[5]  Gabriele Eichfelder,et al.  Characterization of properly optimal elements with variable ordering structures , 2016 .

[6]  J. Dutta,et al.  ON APPROXIMATE MINIMA IN VECTOR OPTIMIZATION , 2001 .

[7]  Xiaoqi Yang,et al.  Characterizations of Variable Domination Structures via Nonlinear Scalarization , 2002 .

[8]  V. Novo,et al.  On Approximate Efficiency in Multiobjective Programming , 2006, Math. Methods Oper. Res..

[9]  Refail Kasimbeyli,et al.  Properly optimal elements in vector optimization with variable ordering structures , 2014, J. Glob. Optim..

[10]  Wojtek Michalowski,et al.  Incorporating wealth information into a multiple criteria decision making model , 2003, Eur. J. Oper. Res..

[11]  Frank Deinzer,et al.  Automatic Robust Medical Image Registration Using a New Democratic Vector Optimization Approach with Multiple Measures , 2009, MICCAI.

[12]  Refail Kasimbeyli,et al.  Conic Scalarization Method in Multiobjective Optimization and Relations with Other Scalarization Methods , 2015, MCO.

[13]  P. Yu Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives , 1974 .

[14]  Gabriele Eichfelder,et al.  Ekeland's variational principle for vector optimization with variable ordering structure , 2014 .

[15]  Refail Kasimbeyli A conic scalarization method in multi-objective optimization , 2013, J. Glob. Optim..

[16]  Refail Kasimbeyli,et al.  A two-objective mathematical model without cutting patterns for one-dimensional assortment problems , 2011, J. Comput. Appl. Math..

[17]  Dick den Hertog,et al.  Approximating the Pareto Set of Multiobjective Linear Programs Via Robust Optimization , 2012, Oper. Res. Lett..

[18]  Daniel Vanderpooten,et al.  Approximate Pareto sets of minimal size for multi-objective optimization problems , 2015, Oper. Res. Lett..

[19]  Refail Kasimbeyli,et al.  A Nonlinear Cone Separation Theorem and Scalarization in Nonconvex Vector Optimization , 2009, SIAM J. Optim..

[20]  César Gutiérrez,et al.  A Unified Approach and Optimality Conditions for Approximate Solutions of Vector Optimization Problems , 2006, SIAM J. Optim..

[21]  Refail Kasimbeyli,et al.  Combined forecasts in portfolio optimization: A generalized approach , 2012, Comput. Oper. Res..

[22]  Rafail N. Gasimov,et al.  Separation via polyhedral conic functions , 2006, Optim. Methods Softw..

[23]  P. Loridan ε-solutions in vector minimization problems , 1984 .