We solve a general vector variational inequality problem in a finitedimensional setting, where only approximation sequences are known instead of exact values of the cost mapping and feasible set. We establish a new equivalence property, which enables us to replace each vector variational inequality with a scalar set-valued variational inequality. Then, we approximate the scalar set-valued variational inequality with a sequence of penalized problems, and we study the convergence of their solutions to solutions of the original one
Bianchi, M., Konnov, I., Pini, R. (2018). Limit vector variational inequality problems via scalarization. JOURNAL OF GLOBAL OPTIMIZATION, 72(3), 579-590 [10.1007/s10898-018-0657-7].
Limit vector variational inequality problems via scalarization
Pini, R.
2018
Abstract
We solve a general vector variational inequality problem in a finitedimensional setting, where only approximation sequences are known instead of exact values of the cost mapping and feasible set. We establish a new equivalence property, which enables us to replace each vector variational inequality with a scalar set-valued variational inequality. Then, we approximate the scalar set-valued variational inequality with a sequence of penalized problems, and we study the convergence of their solutions to solutions of the original one
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LMVVIS.pdf
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