# A note on Minty type vector variational inequalities

Giovanni P. Crespi; Ivan Ginchev; Matteo Rocca

RAIRO - Operations Research - Recherche Opérationnelle (2005)

- Volume: 39, Issue: 4, page 253-273
- ISSN: 0399-0559

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topCrespi, Giovanni P., Ginchev, Ivan, and Rocca, Matteo. "A note on Minty type vector variational inequalities." RAIRO - Operations Research - Recherche Opérationnelle 39.4 (2005): 253-273. <http://eudml.org/doc/244721>.

@article{Crespi2005,

abstract = {The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space $Y$ are introduced. Under quasiconvexity assumptions we show that solutions of generalized variational inequality and of the primitive optimization problem are equivalent. Finally, we discuss the possibility to generalize the scheme of this paper to get further applications in vector optimization.},

author = {Crespi, Giovanni P., Ginchev, Ivan, Rocca, Matteo},

journal = {RAIRO - Operations Research - Recherche Opérationnelle},

keywords = {minty vector variational inequality; existence of solutions; increasing-along-rays property; vector optimization; Minty vector variational inequality},

language = {eng},

number = {4},

pages = {253-273},

publisher = {EDP-Sciences},

title = {A note on Minty type vector variational inequalities},

url = {http://eudml.org/doc/244721},

volume = {39},

year = {2005},

}

TY - JOUR

AU - Crespi, Giovanni P.

AU - Ginchev, Ivan

AU - Rocca, Matteo

TI - A note on Minty type vector variational inequalities

JO - RAIRO - Operations Research - Recherche Opérationnelle

PY - 2005

PB - EDP-Sciences

VL - 39

IS - 4

SP - 253

EP - 273

AB - The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space $Y$ are introduced. Under quasiconvexity assumptions we show that solutions of generalized variational inequality and of the primitive optimization problem are equivalent. Finally, we discuss the possibility to generalize the scheme of this paper to get further applications in vector optimization.

LA - eng

KW - minty vector variational inequality; existence of solutions; increasing-along-rays property; vector optimization; Minty vector variational inequality

UR - http://eudml.org/doc/244721

ER -

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