LIU Shuang, MO Dingyong, ZHOU Zhiang. Vector Variational-Like Inequalities and Vector Optimization Problems Involving ρ-(η,d)-B Invexity on Riemannian Manifolds[J]. Applied Mathematics and Mechanics, 2020, 41(4): 458-466. doi: 10.21656/1000-0887.400227
Citation: LIU Shuang, MO Dingyong, ZHOU Zhiang. Vector Variational-Like Inequalities and Vector Optimization Problems Involving ρ-(η,d)-B Invexity on Riemannian Manifolds[J]. Applied Mathematics and Mechanics, 2020, 41(4): 458-466. doi: 10.21656/1000-0887.400227

Vector Variational-Like Inequalities and Vector Optimization Problems Involving ρ-(η,d)-B Invexity on Riemannian Manifolds

doi: 10.21656/1000-0887.400227
Funds:  The National Natural Science Foundation of China(11861002)
  • Received Date: 2019-07-27
  • Rev Recd Date: 2019-11-19
  • Publish Date: 2020-04-01
  • A class of optimality problems involving the generalized directional derivatives were studied on Riemannian manifolds. Firstly, by means of the generalized directional derivative, three concepts of the ρ-(η,d)-B invex function, the pseudo ρ-(η,d)-B invex function and the quasi ρ-(η,d)-B invex function on Riemannian manifolds were introduced. Secondly, the relations between the solution to variational inequalities and the solution to the optimization problem on Riemannian manifolds were discussed. Finally, the Kuhn-Tucker sufficient condition for the optimality problem was established.
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