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Research Paper | Mathematics | Volume 15 Issue 4, April 2026 | Pages: 125 - 140 | India
Optimality Conditions and Duality Results for Composite Vector Optimization Problem over Cones
Abstract: This study investigates optimality conditions and duality results for a class of composite vector optimization problems defined over cones. The objective and constraint functions are formulated as compositions of vector functions, and the analysis is conducted within a convex cone framework. Using Fenchel-Lagrange duality and conjugate function techniques, necessary and sufficient conditions are derived for a point to be a weak minimum. A corresponding vector dual problem is formulated, and both weak and strong duality results are established under appropriate convexity and constraint qualification assumptions. The results extend existing theories in composite optimization and provide a unified framework for analyzing such problems using conjugate duality methods.
Keywords: Composite vector optimization, Cone optimization, Fenchel-Lagrange duality, Conjugate functions, Weak efficiency, Convex analysis, Multiobjective optimization, Duality theory
How to Cite?: Pooja Louhan, Mritunjay Kumar, "Optimality Conditions and Duality Results for Composite Vector Optimization Problem over Cones", Volume 15 Issue 4, April 2026, International Journal of Science and Research (IJSR), Pages: 125-140, https://www.ijsr.net/getabstract.php?paperid=SR26328144044, DOI: https://dx.dx.doi.org/10.21275/SR26328144044