A projected subgradient method for solving generalized mixed variational inequalities. (English) Zbl 1154.58307

Xia, Fu-Quan; Huang, Nan-Jing; Liu, Zhi-Bin

Oper. Res. Lett. 36, No. 5, 637-642 (2008).

Summary: We consider the projected subgradient method for solving generalized mixed variational inequalities. In each step, we choose an \(\varepsilon _k\)-subgradient \(u^k\) of the function \(f\) and \(w^k\) in a set-valued mapping \(T\), followed by an orthogonal projection onto the feasible set. We prove that the sequence is weakly convergent.

MSC:

58E35	Variational inequalities (global problems) in infinite-dimensional spaces
49J40	Variational inequalities

Keywords:

iterative scheme; projected subgradient method; set-valued mapping; paramonotonicity; \(\varepsilon _k\)-subgradient

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