Some cone separation results and applications
DOI:
https://doi.org/10.33993/jnaat371-873Keywords:
cone separation results, cone enlargements, vector optimizationAbstract
In this note we present some cone separation results in infinite dimensional spaces. Our approach is mainly based on two different types of cone outer approximation. Then we consider an application to vector optimization.Downloads
References
Bednarczuk, E., Stability analysis for parametric vector optimization problems, Dissertationes Mathematicae, 442, pp. 1-126, 2006, https://doi.org/10.4064/dm442-0-1 DOI: https://doi.org/10.4064/dm442-0-1
Dauer, J.P. and Saleh, O.A., A characterization of proper minimal points as solutions of sublinear optimization problems, J. Math. Anal. Appl., 178, pp. 227-246, 1993, https://doi.org/10.1006/jmaa.1993.1303 DOI: https://doi.org/10.1006/jmaa.1993.1303
Durea, M. and Dutta, J., Lagrange multipliers for Pareto minima in general Banach spaces, Pacific Journal of Optimization, to appear.
Durea, M. and Tammer, C., Fuzzy necessary optimality conditions for vector optimization problems, Optimization, to appear., https://doi.org/10.1080/02331930701761615 DOI: https://doi.org/10.1080/02331930701761615
Göpfert, A., Riahi, H., Tammer, C. and Zălinescu, C., Variational Methods in Partially Ordered Spaces, Springer, Berlin, 2003, https://doi.org/10.1007/b97568 DOI: https://doi.org/10.1007/b97568
Henig, M.I., A cone separation theorem, Journal of Optimization Theory and Applications, 36, pp. 451-455, 1982, https://doi.org/10.1007/bf00934357 DOI: https://doi.org/10.1007/BF00934357
Jahn, J., Vector Optimization: Theory, Applications and Extensions, Springer, Berlin, 2004. DOI: https://doi.org/10.1007/978-3-540-24828-6
Krasnosel'skĭi, M.A., Positive Solutions on Operator Equations, Noordhoff, Groningen, 1964.
Mordukhovich, B.S., Variational Analysis and Generalized Differentiation, Vol. I: Basic Theory, Vol. II: Applications, Springer, Berlin, 2006,
Luc, D.T. and Penot J.P., Convergence of asymptotic directions, Trans. Amer. Math. Soc., 353, pp. 4095-4121, 2001, https://doi.org/10.1090/s0002-9947-01-02664-2 DOI: https://doi.org/10.1090/S0002-9947-01-02664-2
Zălinescu, C., Stability for a class of nonlinear optimization problems and applications, in: Nonsmooth Optimization and Related Topics (Erice, 1988), Plenum, New York, pp. 437-458, 1989, https://doi.org/10.1007/978-1-4757-6019-4_26 DOI: https://doi.org/10.1007/978-1-4757-6019-4_26
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.