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Algorithm for solving a new class of generalized nonlinear implicit quasi-variational inclusions in Banach spaces. (English) Zbl 1169.65066
A new class of generalized nonlinear implicit quasi-variational inclusions with general $H$-monotone operator in Banach spaces is introduced and analyzed. An iterative algorithm based on the proximal mapping and Nadler’s theorem for solving this problem is suggested and studied. An existence result for the solution of the problem and the convergence of the iterative sequences are proved.

65K10Optimization techniques (numerical methods)
49J40Variational methods including variational inequalities
49J27Optimal control problems in abstract spaces (existence)
Full Text: DOI
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