Abstract
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.
Keywords
PiecewiseQuadratic equationMathematicsSet (abstract data type)Decision makerQuadratic functionDual (grammatical number)Mathematical optimizationPoint (geometry)Neighbourhood (mathematics)Quadratic programmingApplied mathematicsPiecewise linear functionComputer scienceMathematical analysisOperations researchGeometry
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Publication Info
- Year
- 2001
- Type
- article
- Volume
- 10
- Issue
- 1
- Pages
- 35-47
- Citations
- 16
- Access
- Closed
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Cite This
Margaret M. Wiecek,
Wei Chen,
Jinhuan Zhang
(2001).
Piecewise quadratic approximation of the non‐dominated set for bi‐criteria programs.
Journal of Multi-Criteria Decision Analysis
, 10
(1)
, 35-47.
https://doi.org/10.1002/mcda.287
Identifiers
- DOI
- 10.1002/mcda.287