Auxiliary problem principle extended to variational inequalities
Journal of Optimization Theory and Applications
Mathematical Programming: Series A and B
SIAM Journal on Control and Optimization
Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming
Mathematics of Operations Research
Family of perturbation methods for variational inequalities
Journal of Optimization Theory and Applications
Progressive regularization of variational inequalities and decomposition algorithms
Journal of Optimization Theory and Applications
Proximal Point Approach and Approximation of Variational Inequalities
SIAM Journal on Control and Optimization
SIAM Journal on Optimization
Proximal Point Methods and Nonconvex Optimization
Journal of Global Optimization
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An extension of the auxiliary problem principle to variational inequalities with non-symmetric multi-valued operators in Hilbert spaces is studied. This extension concerns the case that the operator is split into the sum of a single-valued operator \cal F, possessing a kind of pseudo Dunn property, and a maximal monotone operator \cal L. The current auxiliary problem is k constructed by fixing \cal F at the previous iterate, whereas \cal L (or its single-valued approximation {\cal L}k) k is considered at a variable point. Using auxiliary operators of the form {\cal L}k+χ\nabla h, with χk0, the standard for the auxiliary problem principle assumption of the strong convexity of the function h can be weakened exploiting mutual properties of \cal L and h. Convergence of the general scheme is analyzed and some applications are sketched briefly.