On nonsmooth multiobjective semi-infinite mathematical programming problems with vanishing constraints on Hadamard manifolds: saddle point optimality and Lagrange duality
Journal of Decision Making and Healthcare, Volume 2, Issue 3, December 2025, Pages: 163–184
ARNAV GHOSH
Center for General Education, China Medical University, Taichung, Taiwan
JEN-CHIH YAO
Center for General Education, China Medical University, Taichung, Taiwan
Academy of Romanian Scientists, 50044 Bucharest, Romania
Abstract
In this article, we investigate a class of nonsmooth multiobjective semi-infinite programming problems with vanishing constraints (in short, NSIMOPVC) on Hadamard manifolds. We introduce the scalarized Lagrange-type dual problem and the vector Lagrange-type dual problem related to NSIMOPVC in the framework of Hadamard manifolds. We derive weak and strong duality theorems relating NSIMOPVC and the corresponding dual problems under suitable geodesic convexity assumptions. Moreover, we establish scalarized saddle point optimality conditions as well as vector saddle point optimality conditions for NSIMOPVC in the setting of Hadamard manifolds. To the best of our knowledge, this is for the first time that saddle point optimality criteria and Lagrange duality for NSIMOPVC have been investigated on Hadamard manifolds.
Cite this Article as
Arnav Ghosh and Jen-Chih Yao, On nonsmooth multiobjective semi-infinite mathematical programming problems with vanishing constraints on Hadamard manifolds: saddle point optimality and Lagrange duality, Journal of Decision Making and Healthcare, 2(3), 163–184, 2025