Augmented Lagrangian and Tchebycheff Approaches in Multiple Objective Programming

Authors:
Jørgen Tind;Margaret M. Wiecek
Affiliations:
Department of Operations Research, Institute for Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen O, Denmark (e-mail: tind@math.ku.dk);Department of Mathematical Sciences, Clemson University, Martin Hall, Clemson, SC 29634, USA (e-mail: wmalgor@clemson.edu)
Venue:
Journal of Global Optimization
Year:
1999

Citing 5
Cited 1

A modified weighted Tchebycheff metric for multiple objective programming

Computers and Operations Research
Linear programming and network flows (2nd ed.)

Linear programming and network flows (2nd ed.)
Duality in nonlinear multiobjective programming using augmented Lagrangian functions

Journal of Optimization Theory and Applications
Generating well-behaved utility functions for compromise programming

Journal of Optimization Theory and Applications
Efficiency and Solution Approaches to Bicriteria Nonconvex Programs

Journal of Global Optimization

Computing trade-offs in robust design: Perspectives of the mean squared error

Computers and Industrial Engineering

Quantified Score

Hi-index	0.00

Visualization

Abstract

Relationships between the Tchebycheff scalarization and the augmented Lagrange multiplier technique are examined in the framework of general multiple objective programs (MOPs). It is shown that under certain conditions the Tchebycheff method can be represented as a quadratic weighted-sums scalarization of the MOP, that is, given weight values in the former, the coefficients of the latter can be found so that the same efficient point is selected. Analysis for concave and linear MOPs is included. Resulting applications in multiple criteria decision making are also discussed.