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Zbl 1155.90018
Gong, X.H.
Connectedness of the solution sets and scalarization for vector equilibrium problems. (English)
[J] J. Optim. Theory Appl. 133, No. 2, 151-161 (2007). ISSN 0022-3239; ISSN 1573-2878/e

The author studies vector equilibrium problems. The set of weak-, Henning-, and super-efficient solutions are considered as well as the new concept of globally efficient and cone-benson efficient solutions. Scalarization results for these solution sets are derived and conditions are given under which some of these sets coincide. Based on the scalarization results it is shown under which conditions the solution sets are connected or path connected.
[Georg Still (Enschede)]

MSC 2000:: *90C33 Complementarity problems
47N10 Appl. of operator theory in optimization, math. programming, etc.
49J40 Variational methods including variational inequalities

Keywords: vector equilibrium problems; globally efficient solutions; cone-benson efficient solutions; scalarization; path connectedness

Cited in: Zbl 1238.49018 Zbl 1176.49019

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