În cadrul seminarului grupului de cercetare Analiză și Optimizare, prof. dr. Christiane Tammer, de la Martin-Luther-Universität Halle-Wittenberg (Germania), va susține joi, 26 iunie 2025, de la ora 12.30, în sala Pi, clădirea Mathematica, prezentarea

Construction of Vector-Valued Weak Separation Functions with Applications to Conjugate Duality in Vector Optimization

(joint work with Siqi Wang and Chaoli Yao, Hainan University, China).

Rezumatul prezentării:

We establish a united framework for conjugate duality theory for constrained vector optimization problems using vector-valued nonlinear weak separation and topical functions (see [1]). The advantage of this new approach is that we compare objective function values of the primal and dual problem in the (extended) image space of the primal objective function. Furthermore, in the formulation of the duality statements, we avoid a scalarization. In our previous paper [2], collections of scalar weak separation functions were proposed for image space analysis, while this talk is concerned with vector-valued weak separation functions. Using vector-valued separation functions, the dual model is given for the vector optimization problem directly, unlike the previous work [3], where the primal problem was scalarized. We study a pair of a primal vector-valued problem and a dual set-valued problem and derive weak as well as strong duality assertions for this pair.

References

[1] Rubinov, A.M. and I. Singer (2001), Topical and sub-topical functions, downward sets and abstract convexity, Optimization, vol.50, n.5-6, pp.307-351.
[2] Yao, C.L. and C. Tammer (2023), Weak separation functions constructed by Gerstewitz and topical functions with applications in conjugate duality, J. Nonlinear Var. Anal., vol. 7, n. 5, pp.859-896.
[3] Yao, C.L. and S.J. Li (2020), Conjugate duality for constrained vector optimization in abstract convex frame. Numer. Func. Anal. Optim., vol.40, pp. 1242-1267

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