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Piecewise quadratic approximation of the non‐dominated set for bi‐criteria programs
Author(s) -
Wiecek Margaret M.,
Chen Wei,
Zhang Jinhuan
Publication year - 2001
Publication title -
journal of multi‐criteria decision analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.462
H-Index - 47
eISSN - 1099-1360
pISSN - 1057-9214
DOI - 10.1002/mcda.287
Subject(s) - piecewise , quadratic equation , mathematics , set (abstract data type) , decision maker , quadratic function , dual (grammatical number) , mathematical optimization , point (geometry) , neighbourhood (mathematics) , quadratic programming , piecewise linear function , computer science , mathematical analysis , operations research , geometry , art , literature , programming language
Abstract A procedure to approximate the non‐dominated set for general (continuous) bi‐criteria programs is proposed. The piecewise approximation is composed of quadratic curves, each of which is developed locally in a neighbourhood of a non‐dominated point of interest and based on primal–dual relationships associated with the weighted Tchebycheff scalarization of the original problem. The approximating quadratic functions, in which decision maker's preferences are represented, give a closed‐form description of the non‐dominated set. A numerical example is included. Copyright © 2001 John Wiley & Sons, Ltd.