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The Effects of Adding Objectives to an Optimization Problem on the Solution Set

Joerg Fliege (fliegej***at***bham.ac.uk)

Abstract: Suppose that for a given optimisation problem (which might be multicriteria problem or a single-criteron problem), an additional objective function is introduced. How does the the set of solutions, i.~e.\ the set of efficient points change when instead of the old problem the new multicriteria problem is considered? How does the set of properly efficient points, the set of weakly efficient points and the set of strictly efficient points change? And what kind of effects occur in the value space? This paper answers these questions under various suitable assumptions.

Keywords: multicriteria optimisation, vector optimisation, efficient points, Pareto points, stability

Category 1: Other Topics (Multi-Criteria Optimization )

Citation: Preprint 2006/01, School of Mathematics, The University of Birmingham, Edbagston, Birmingham B15 2TT, UK. January 2006

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Entry Submitted: 01/17/2006
Entry Accepted: 01/19/2006
Entry Last Modified: 01/22/2006

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