Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 651-660.

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Approximate Optimality Conditions and Mixed Type Duality for a Class of Non-Convex Optimization Problems

Jiaolang Wang(),Donghui Fang*()   

  1. College of Mathematics and Statistics, Jishou University, Hunan Jishou 416000
  • Received:2021-08-12 Online:2022-06-26 Published:2022-05-09
  • Contact: Donghui Fang;
  • Supported by:
    the NSFC(11861033);the NSF of Hunan Province(2020JJ4494);the Scientific Research Fund of Jishou University(Jdy20069);the Scientific Research Fund of Jishou University(JGY202139)


By using the properties of the Fréchet subdifferentials, we first introduce a new constraint qualification and then establish some approximate optimality conditions for the non-convex constrained optimization problem with objective function and/or constraint function being α-convex function. Moreover, some results for the weak duality, strong duality and converse-like duality theorems between this non-convex optimization problem and its mixed type dual problem are also given.

Key words: Non-convex constraint optimization problem, Constraint qualification, Approximate optimality conditions, Mixed type duality

CLC Number: 

  • O224