Points of Efficiency in Vector Optimization with Increasing-along-rays Property and Minty Variational Inequalities

Giovanni P. Crespi (), Ivan Ginchev () and Matteo Rocca ()
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Giovanni P. Crespi: Université de la Vallé d’Aoste
Ivan Ginchev: Technical University of Varna
Matteo Rocca: University of Insubria

A chapter in Generalized Convexity and Related Topics, 2007, pp 209-226 from Springer

Abstract: Summary Minty variational inequalities are studied as a tool for vector optimization. Instead of focusing on vector inequalities, we propose an approach through scalarization which allows to construct a proper variational inequality type problem to study any concept of efficiency in vector optimization. This general scheme gives an easy and consistent extension of scalar results, providing also a notion of increasing along rays vector function. This class of generalized convex functions seems to be intimately related to the existence of solutions to a Minty variational inequality in the scalar case, we now extend this fact to vector case. Finally, to prove a reversal of the main theorem, generalized quasiconvexity is considered and the notion of *-quasiconvexity plays a crucial role to extend scalar evidences. This class of functions, indeed, guarantees a Minty-type variational inequality is a necessary and sufficient optimality condition for several kind of efficient solution.

Keywords: Minty variational inequalities; vector optimization; generalized quasiconvexity; scalarization (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-540-37007-9_12

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DOI: 10.1007/978-3-540-37007-9_12

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