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

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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, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:570918
    DOI: 10.1155/2013/570918
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    References listed on IDEAS

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