A note on strong pseudoconvexity

Vsevolod Ivanov

Open Mathematics (2008)

  • Volume: 6, Issue: 4, page 576-580
  • ISSN: 2391-5455

Abstract

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A strongly pseudoconvex function is generalized to non-smooth settings. A complete characterization of the strongly pseudoconvex radially lower semicontinuous functions is obtained.

How to cite

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Vsevolod Ivanov. "A note on strong pseudoconvexity." Open Mathematics 6.4 (2008): 576-580. <http://eudml.org/doc/269547>.

@article{VsevolodIvanov2008,
abstract = {A strongly pseudoconvex function is generalized to non-smooth settings. A complete characterization of the strongly pseudoconvex radially lower semicontinuous functions is obtained.},
author = {Vsevolod Ivanov},
journal = {Open Mathematics},
keywords = {Generalized convexity; strict pseudoconvexity; nonsmooth analysis; nonsmooth optimization; Dini directional derivatives},
language = {eng},
number = {4},
pages = {576-580},
title = {A note on strong pseudoconvexity},
url = {http://eudml.org/doc/269547},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Vsevolod Ivanov
TI - A note on strong pseudoconvexity
JO - Open Mathematics
PY - 2008
VL - 6
IS - 4
SP - 576
EP - 580
AB - A strongly pseudoconvex function is generalized to non-smooth settings. A complete characterization of the strongly pseudoconvex radially lower semicontinuous functions is obtained.
LA - eng
KW - Generalized convexity; strict pseudoconvexity; nonsmooth analysis; nonsmooth optimization; Dini directional derivatives
UR - http://eudml.org/doc/269547
ER -

References

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  2. [2] Diewert W.E., Avriel M., Zang I., Nine kinds of quasiconcavity and concavity, J. Econom. Theory, 1981, 25, 397–420 http://dx.doi.org/10.1016/0022-0531(81)90039-9 Zbl0483.26007
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  4. [4] Hadjisavvas N., Schaible S., On strong pseudomonotonicity and (semi)strict quasimonotonicity, J. Optim. Theory Appl., 1995, 85,741–742 http://dx.doi.org/10.1007/BF02193065 Zbl0833.90104
  5. [5] Ivanov V.I., First order characterizations of pseudoconvex functions, Serdica Math. J., 2001, 27, 203–218 Zbl0982.26009
  6. [6] Karamardian S., Complementarity problems over cones with monotone and pseudomonotone maps., J. Optim. Theory Appl., 1976, 18, 445–454 http://dx.doi.org/10.1007/BF00932654 Zbl0304.49026
  7. [7] Karamardian S., Schaible S., Seven kinds of monotone maps, J. Optim. Theory Appl., 1990, 66, 37–46 http://dx.doi.org/10.1007/BF00940531 Zbl0679.90055
  8. [8] Komlósi S., Generalized monotonicity in nonsmooth analysis, In: Komlósi S., Rapcsák T., Schaible S. (Eds.), Generalized convexity, Springer Verlag, Heidelberg, 1994, 263–275 Zbl0811.49013
  9. [9] Mishra M.S., Nanda S., Acharya D., Strong pseudo-convexity and symmetric duality in nonlinear programming, J. Aust. Math. Soc. Ser. B, 1985, 27, 238–244 http://dx.doi.org/10.1017/S0334270000004884 Zbl0584.90087
  10. [10] Ponstein J., Seven kinds of convexity, SIAM Review, 1967, 9, 115–119 http://dx.doi.org/10.1137/1009007 Zbl0164.06501
  11. [11] Weir T., On strong pseudoconvexity in nonlinear programming duality, Opsearch, 1990, 27, 117–121 Zbl0713.90058
  12. [12] Yang Y., On strong pseudoconvexity and strong pseudomonotonicity, Numer. Math. J. Chinese Univ., 2000, 22, 141–146 Zbl0955.46010

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