Abstract

We present second-order necessary and sufficient conditions for weak efficiency of nonsmooth semi-infinite multiobjective programming involving inequality, equality and set constraints in terms of the Páles-Zeidan second-order directional derivatives. Sufficient optimality conditions are established in two cases. They include the case without assumptions on generalized convexity and the case with assumptions on the 2-generalized convexity together with second-order duality theorems of Mond-Weir type.

Author information

Contact details are reproduced from the original publication and may be historical.

Do Van Luu

Institute of Mathematics and Applied Sciences, Thang Long University, Hanoi, Vietnam

dvluu@math.ac.vn

Keywords

  • Second-order necessary efficiency conditions
  • Pales-Zeidan second-order directional derivatives
  • first and second-order tangent vectors
  • second-order constraint qualifications
  • nonsmooth semi-infinite multiobjective optimization problem

Mathematics Subject Classification

90C46, 90C29

Suggested citation

D. V. Luu, N. L. Tung. “Second-Order Necessary and Sufficient Efficiency Conditions for Nonsmooth Semi-Infinite Multiobjective Optimization Problems.” Journal of Convex Analysis 31 (2024), No. 4, 1189–1202. https://doi.org/10.68381/jca31058

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Published by Heldermann Verlag, 2024. Rights now held by Banach Press.