The Tikhonov regularization for vector equilibrium problems
We consider vector equilibrium problems in real Banach spaces and study their regularized problems. Based on cone continuity and generalized convexity properties of vector-valued mappings, we propose general conditions that guarantee existence of solutions to such problems in cases of monotonicity a...
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| Veröffentlicht in: | Computational optimization and applications 2021-04, Vol.78 (3), p.769-792 |
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| container_title | Computational optimization and applications |
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| creator | Anh, Lam Quoc Duy, Tran Quoc Muu, Le Dung Tri, Truong Van |
| description | We consider vector equilibrium problems in real Banach spaces and study their regularized problems. Based on cone continuity and generalized convexity properties of vector-valued mappings, we propose general conditions that guarantee existence of solutions to such problems in cases of monotonicity and nonmonotonicity. First, our study indicates that every Tikhonov trajectory converges to a solution to the original problem. Then, we establish the equivalence between the problem solvability and the boundedness of any Tikhonov trajectory. Finally, the convergence of the Tikhonov trajectory to the least-norm solution of the original problem is discussed. |
| doi_str_mv | 10.1007/s10589-020-00258-z |
| format | Article |
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| source | EBSCOhost Business Source Complete; SpringerLink Journals - AutoHoldings |
| subjects | Banach spaces Convergence Convex and Discrete Geometry Convexity Management Science Mathematics Mathematics and Statistics Operations Research Operations Research/Decision Theory Optimization Regularization Statistics |
| title | The Tikhonov regularization for vector equilibrium problems |
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