Vector optimization with cone semilocally preinvex functions
DOI:
https://doi.org/10.11121/ijocta.01.2014.00162Keywords:
Vector optimization, semilocally preinvex functions, cones, optimality, duality.Abstract
In this paper we introduce cone semilocally preinvex, cone semilocally quasi preinvex and cone semilocally pseudo preinvex functions and study their properties. These functions are further used to establish necessary and sufficient optimality conditions for a vector minimization problem over cones. A Mond-Weir type dual is formulated for the vector optimization problem and various duality theorems are proved.
Downloads
References
Ewing G.M., Sufficient Conditions for Global Minima of Suitable Convex Functional from Variational and Control Theory. SIAM Rev. 19, 202-220 (1977). CrossRef
Illes, T., Kassay, G., Theorems of the Alternative and Optimality Conditions for Convexlike and General Convexlike Programming. Journal of Optimization Theory and Applications 101(2), 243-257 (1999). CrossRef
Kaul, R.N., Kaur, S., Generalization of Convex and Related Functions. European Journal of Operational Research 9, 369-377 (1982). CrossRef
Kaul, R.N., Kaur, S., Sufficient Optimality Conditions using Generalized Convex Functions. Opsearch 19, 212-224 (1982).
Kaul, R.N., Kaur, S., Generalized Convex Functions, Properties, Optimality and Duality. Technical Report Sol., 84-4, Stanford University, California (1984).
Kaul, R.N., Lyall, V., Kaur, S., Semilocal Pseudolinearity and Efficiency. European Journal of Operational Research 36, 402-409 (1988). CrossRef
Kaur, S., Theoretical Studies in Mathematical Programming. Ph.D. Thesis, University of Delhi, Delhi, India (1983).
Gupta, I., Vartak, M.N., Kuhn-Tucker and Fritz John Type Sufficient Optimality Conditions for Generalized Semilocally Convex Programs. Opsearch 26, 11-27 (1989).
Mukherjee, R.N., Mishra, S.K., Multiobjective Programming with Semilocally Convex Functions. Journal of Mathematical Analysis and Applications. 199, 409-424 (1996). CrossRef
Preda, V., Optimality Conditions and Duality in Multiobjective Programming Involving Semilocally Convex and Related Functions. Optimization 36, 219-230 (1996). CrossRef
Preda, V., Optimality and Duality in Fractional Multiobjective Programming involving Semilocally Preinvex and Related Functions. Journal of Mathematical Analysis and Applications 288, 365-382 (2003). CrossRef
Preda V., Stancu-Minasian, J.M., Duality in Multiobjective Programming involving Semilocally Preinvex and Related Functions. Glas. Math. 32, 153-165 (1997).
Stancu-Minasian, J.M., Optimality and Duality in Fractional Programming involving Semilocally Preinvex and Related Functions. Journal of Information and Optimization Science 23, 185-201 (2002). CrossRef
Suneja, S.K., Gupta, S., Duality in Nonlinear Programming involving Semilocally Convex and Related Functions. Optimization 28, 17-29 (1993). CrossRef
Suneja, S.K., Gupta, S., Vani, Optimality and Duality in Multiobjective Nonlinear programming involving -Semilocally Preinvex and Related Functions. Opsearch 44(1), 27-40 (2007).
Weir, T., Programming with Semilocally Convex Functions. Journal of Mathematical Analysis and Applications 168 (1-2), 1-12 (1992). CrossRef
Downloads
Published
How to Cite
Issue
Section
License
Articles published in IJOCTA are made freely available online immediately upon publication, without subscription barriers to access. All articles published in this journal are licensed under the Creative Commons Attribution 4.0 International License (click here to read the full-text legal code). This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.
Under the Creative Commons Attribution 4.0 International License, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in IJOCTA, so long as the original authors and source are credited.
The readers are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material
- for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
under the following terms:
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
This work is licensed under a Creative Commons Attribution 4.0 International License.
