Proximity control in bundle methods for convex
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Convergence of some algorithms for convex minimization
Mathematical Programming: Series A and B - Special issue: Festschrift in Honor of Philip Wolfe part II: studies in nonlinear programming
Variable metric bundle methods: from conceptual to implementable forms
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Mathematical Programming: Series A and B
Approximate iterations in Bregman-function-based proximal algorithms
Mathematical Programming: Series A and B
Mathematics of Operations Research
A Generalized Proximal Point Algorithm for the Variational Inequality Problem in a Hilbert Space
SIAM Journal on Optimization
Bregman functions and auxiliary problem principle
Optimization Methods & Software
Computer Aided Geometric Design
Hi-index | 0.00 |
In this paper two versions of the relaxed proximal point schemes for solving variational inequalities with maximal monotone and multi-valued operators are investigated. The first one describes an algorithm with an adaptive choice of the relaxation parameter and is combined with the use of ε-enlargements of multi-valued operators. The second one makes use of Bregman functions in order to construct relaxed proximal point algorithms with an interior point effect. For both algorithms convergence is proved under a numerically tractable error summability criterion, based on the ideas in [R. T. Rockafellar, Augmented Lagrangians and applications of the proximal point algorithm in convex programming, Math. Oper. Res. 1(2) (1976), pp. 97-116.] [R. T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optim. 14(5) (1976), pp. 877-898.] Finally, some numerical aspects are discussed and test examples show the performance of the first algorithm when applying to non-smooth optimization problems.