The Pascoletti–Serafini Scalarization Scheme and Linear Vector Optimization
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The Pascoletti–Serafini scalarization scheme for general vector optimization problems is studied. It is specified to linear vector optimization to give minimal representation formulae for the weakly efficient solution set and the efficient solution set. Several facts on connectedness of the solution sets of Pascoletti–Serafini’s scalar auxiliary problems, both for linear vector optimization and for nonlinear vector optimization, are established.
KeywordsVector optimization Linear vector optimization The Pascoletti–Serafini scalarization Representation formula Solution connectedness
This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2011.01. The first author was supported in part by Department of Information Technology, Le Qui Don University. The authors are indebted to the three anonymous referees for their detailed remarks and valuable suggestions. The counterexample given in Remark 2.1 is due to one of the referees. We would like also to thank Mr. Pham Duy Khanh for a useful discussion on the subject.
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