Extended Lorentz Cones and Variational Inequalities on Cylinders

Sándor Zoltán Németh () and Guohan Zhang ()
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Sándor Zoltán Németh: University of Birmingham
Guohan Zhang: University of Birmingham

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 3, No 2, 756-768

Abstract: Abstract Solutions of a variational inequality problem defined by a closed and convex set and a mapping are found by imposing conditions for the monotone convergence with respect to a cone of the Picard iteration corresponding to the composition of the projection onto the defining closed and convex set and the difference in the identity mapping and the defining mapping. One of these conditions is the isotonicity of the projection onto the defining closed and convex set. If the closed and convex set is a cylinder and the cone is an extented Lorentz cone, then this condition can be dropped because it is automatically satisfied. In this case, a large class of affine mappings and cylinders which satisfy the conditions of monotone convergence above is presented. The obtained results are further specialized for unbounded box-constrained variational inequalities. In a particular case of a cylinder with a base being a cone, the variational inequality is reduced to a generalized mixed complementarity problem which has been already considered in Németh and Zhang (J Global Optim 62(3):443–457, 2015).

Keywords: Isotone projections; Cones; Variational inequalities; Picard iteration; Fixed point; 90C33; 47H07; 47H99; 47H09 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-015-0833-6

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