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Kuhn-tucker condition and wolfe duality of preinvex set-valued optimization

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Abstract

The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.

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Authors and Affiliations

  1. Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, 312000, Zhejiang Province, P. R. China

    Sheng Bao-huai Doctor  (盛宝怀) (Professor)

  2. Department of Applied Mathematics, Xidian University, Xi’an, 710071, P. R. China

    Liu San-yang  (刘三阳)

Authors
  1. Sheng Bao-huai Doctor  (盛宝怀)
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  2. Liu San-yang  (刘三阳)
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Correspondence to Sheng Bao-huai Doctor  (盛宝怀).

Additional information

Communicated by ZHANG Shi-sheng

Project supported by the National Natural Science Foundation of China (No.10371024) and the Natural Science Foundation of Zhejiang Province (No.Y604003)

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Sheng, Bh., Liu, Sy. Kuhn-tucker condition and wolfe duality of preinvex set-valued optimization. Appl Math Mech 27, 1655–1664 (2006). https://doi.org/10.1007/s10483-006-1208-z

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  • DOI: https://doi.org/10.1007/s10483-006-1208-z

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Chinese Library Classification

2000 Mathematics Subject Classification

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