Invexity and a Class of Constrained Optimization Problems in Hilbert Spaces

Sandip Chatterjee

DOI Number
-
First page
337
Last page
342

Abstract


In this paper the notion of invexity has been introduced in Hilbert spaces. A class of constrained optimization problems has been proposed under the assumption of invexity. Some of the algebraic properties leading to the optimality criterion of such class of problems has been studied.

Keywords


Convexity ; Invexity ; Frechet Derivative ; Archimedean Order ; Zorn's Lemma

Full Text:

PDF

References


bibitem{1} Anderson E.J. and Nash P., Linear Programming in Infinite Dimensional Spaces, John Willey and Sons. 1987.

bibitem{2} Avriel M. Nonlinear Programming: Analysis and Methods, Prentice Hall, New Jersey. 1976.

bibitem{3} Barbu V., Precupanu T. Convexity and Optimization in Banach Spaces, Springer , 2012.

bibitem{4} Bertsekas D.P. Convex Optimization Theory, Athena Scientific. 2009.

bibitem{5} Ben-Israel A., Mond B. What is Invexity? Journal of Australian Mathematical Society, Ser. B, 28,1, 1-9, 1986.

bibitem{6} Ben-Tal A. On Generalized Means and Generalized Convex Functions, Journal of Optimization Theory and Applications. 21:1-13. 1977.

bibitem{7} Benyamini Y., Lindenstrauss J. Geometric Non-Linear Functional Analysis. Vol.-1, American Mathematical Society, Colloquium Publications.(Vol.48). 2000.

bibitem{8} Borwein J.M.,Lewis A.S. Convex Analysis and Nonlinear Optimization, Springer. 2006.

bibitem{9} Boyd S. and Vendenberghe L. Convex Optimization, Cambridge University Press. 2004.

bibitem{10} Craven B.D., Invex functions and constrained local minima, Bulletin of the Australian Mathematical Society. 24:1-20. 1981.

bibitem{11} Craven B.D.,Glover B.M. Invex functions and duality, Journal of Australian Mathematical Society. Ser. A,39,1-20.1985.

bibitem{12} Hanson M.A. On Sufficiency of Kuhn-Tucker conditions, Journal of Mathematical Analysis and Applications.80,545-550, 1981.

bibitem{13} Hiriart-Urruty J.B. and Lamerachal C., Fundamentals of Convex Analysis. Springer. 2001.

bibitem{14} Jeyakumar V, Mond B, On generalized convex mathematical programming, Journal of Australian Mathematical Society. Series B, 34:43-53. 1992.

bibitem{15} Luenberger D.G., Optimization by Vector Space Methods, John Willey and Sons,.1969.

bibitem{16} Luu D.V., Ha N.X. An Invariant property of invex functions and applications, Acta Mathematica Vietnamica. Vol: 25, 181-193. 2000.

bibitem{17} Martin D.H., The Essence of Invexity, J.O.T.A. 47,1,65-76.1985.

bibitem{18} Mishra S.K., Giorgi G. Invexity and Optimization, Springer-Verlag. 2008.

bibitem{19} Mititelu Stefan., Invex Sets and Preinvex Functions, Journal of Advanced Mathematical Studies. Vol.2, No.2,41-52. 2009.

bibitem{20} Pini R., Invexity and generalized convexity, Optimization. 22,4,513-525. 1991.

bibitem{21} Rockafellar R.T., Convex Analysis, Princeton University Press. 1970.

bibitem{22} Tiel J.V., Convex Analysis-An Introductory Text, John Willey and Sons. 1984.


Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)