Generalized Equilibria with Multivalued Trifunctions and Applications to Uncertain Vector Equilibrium Problems

Pham Huu Sach () and Le Anh Tuan ()
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Pham Huu Sach: Institute of Mathematics, Vietnam Academy of Science and Technology
Le Anh Tuan: Nong Lam University

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 51, 29 pages

Abstract: Abstract This paper provides sufficient conditions for the existence of weak solutions of general vector equilibrium problems described in topological vector spaces by weakly diagonally cone-quasiconvex trifunctions and by possibly nonsemicontinuous and nonconvex-valued/nonclosed-valued multimaps. Our approach is different from the corresponding previous ones: it is new and flexible in the sense that sufficient conditions for the solution existence depend on the choice of a suitable auxiliary multimap which allows us to improve some existing results. We also show that the main results of the paper are useful for studying the existence of robust weak solutions for several problems with uncertain objectives and, in particular, for non-cooperative Nash games with uncertainty.

Keywords: Multimap; Trifunction; Solution existence; Generalized equilibria; Uncertain vector equilibrium problem; 49J40; 47H04; 47H10 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02875-2

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