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| Volume 7, Number 1, April 2006, pp. 39-50 | |||||||||
| Giovanni P. Crespi, Ivan Ginchev, and Matteo Rocca | |||||||||
| Key words: | |||||||||
| generalized convexity, increasing-along-rays property, star-shaped set, Minty variational inequality | |||||||||
| Mathematices Subject Classification: | |||||||||
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| Volume 7, Number 1, April 2006, pp. 39-50 | |||||||||
| Giovanni P. Crespi, Ivan Ginchev, and Matteo Rocca | |||||||||
| Key words: | |||||||||
| generalized convexity, increasing-along-rays property, star-shaped set, Minty variational inequality | |||||||||
| Mathematices Subject Classification: | |||||||||
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| Abstract: | |||
| In this paper we extend to the vector case the notion of increasing-along-rays function. The proposed definition is given by means of a nonlinear scalarization through the so-called oriented distance function from a point to a set.
We prove that the considered class of functions enjoys properties similar to those holding in the scalar case, with regard to optimization problems, relations with (generalized) convex functions and characterization in terms of Minty type variational inequalities. |
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| Increasing-along-rays property for vector functions | ||