Hostname: page-component-599cfd5f84-9drbd Total loading time: 0 Render date: 2025-01-07T07:48:52.082Z Has data issue: false hasContentIssue false
  • English
  • Français

The Strictly Efficient Subgradient of Set-Valued Optimisation

Published online by Cambridge University Press:  17 April 2009

Taiyong Li  and
Yihong Xu
Taiyong Li
Affiliation:
Department of Mathematics, Nanchang University, Nanchang 330031, China
Yihong Xu
Affiliation:
Department of Mathematics, Nanchang University, Nanchang 330031, China
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The subgradient, under strict efficiency, of a set-valued mapping is developed, and the existence of the subgradient is proved. Optimality conditions in terms of Lagrange multipliers for a strictly efficient point are established in the general case and in the case with ic-cone-convexlike data.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 3 , June 2007 , pp. 361 - 371
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Cheng, Y.H. and Fu, W.T., ‘Strong efficiency in a locally convex space’, Math. Meth. Oper. Res. 50 (1999), 373–384.CrossRefGoogle Scholar
[2]Fu, W.T., ‘On approximation families of cones and strictly efficient points’, (in Chinese), Acta. Math. Sinica. 40 (1997), 933–938.Google Scholar
[3]Corley, W., ‘Existence and Lagrange duality for maximization of set-valued functions’, J. Optim. Theory. Appl. 54 (1987), 489–501.CrossRefGoogle Scholar
[4]Gong, X.H., ‘Connectedness of efficient solutions sets for set-valued maps in normed spaces’, J. Optim. Theory. Appl. 83 (1994), 83–96.Google Scholar
[5]Kuk, H., Tanino, T. and Tanaka, M., ‘Sensitivity analysis in vector optimization’, J. Optim. Theory. Appl. 89 (1996), 713–730.CrossRefGoogle Scholar
[6]Lin, L.J., ‘Optimization of set-valued functions’, J. Math. Analysis. Appl. 186 (1994), 30–51.CrossRefGoogle Scholar
[7]Taa, A., ‘Subdifferentials of multifunctions and Lagrange multipliers for multiobjective optimization’, J. Math. Anal. Appl. 283 (2003), 398–415.Google Scholar
[8]Sach, P.H., ‘New generalized convexity notion for set-valued maps and application to vector optimization’, J. Optim. Theory. Appl. 125 (2005), 157–179.Google Scholar
[9]Li, T.Y. and Xu, Y.H., ‘On strict efficiency in set-valued optimization with generalized convexity’, (in Chinese), J. Nanchang Uni. (to appear).Google Scholar