A note on Minty type vector variational inequalities

Giovanni P. Crespi; Ivan Ginchev; Matteo Rocca

RAIRO - Operations Research (2006)

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

Abstract

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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.

How to cite

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Crespi, Giovanni P., Ginchev, Ivan, and Rocca, Matteo. "A note on Minty type vector variational inequalities." RAIRO - Operations Research 39.4 (2006): 253-273. <http://eudml.org/doc/105333>.

@article{Crespi2006,
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},
keywords = {Minty vector variational inequality; existence of solutions; increasing-along-rays property; vector optimization.; vector optimization},
language = {eng},
month = {4},
number = {4},
pages = {253-273},
publisher = {EDP Sciences},
title = {A note on Minty type vector variational inequalities},
url = {http://eudml.org/doc/105333},
volume = {39},
year = {2006},
}

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
DA - 2006/4//
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.; vector optimization
UR - http://eudml.org/doc/105333
ER -

References

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