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Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps

Author

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  • Xiaohong Hu
  • Zhimiao Fang
  • Yunxuan Xiong

Abstract

The concept of the well posedness for a special scalar problem is linked with strictly efficient solutions of vector optimization problem involving nearly convexlike set-valued maps. Two scalarization theorems and two Lagrange multiplier theorems for strict efficiency in vector optimization involving nearly convexlike set-valued maps are established. A dual is proposed and duality results are obtained in terms of strictly efficient solutions. A new type of saddle point, called strict saddle point, of an appropriate set-valued Lagrange map is introduced and is used to characterize strict efficiency.

Suggested Citation

  • Xiaohong Hu & Zhimiao Fang & Yunxuan Xiong, 2013. "Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, April.
    • Handle: RePEc:hin:jnlaaa:570918
    DOI: 10.1155/2013/570918
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