@article {IOPORT.05550707, author = {Auslender, Alfred and Teboulle, Marc}, title = {Projected subgradient methods with non-Euclidean distances for non-differentiable convex minimization and variational inequalities.}, year = {2009}, journal = {Mathematical Programming. Series A. Series B}, volume = {120}, number = {1 (B)}, issn = {0025-5610}, pages = {27-48}, publisher = {Springer-Verlag, Berlin}, doi = {10.1007/s10107-007-0147-z}, abstract = {Summary: We study subgradient projection type methods for solving non-differentiable convex minimization problems and monotone variational inequalities. The methods can be viewed as a natural extension of subgradient projection type algorithms, and are based on using non-Euclidean projection-like maps, which generate interior trajectories. The resulting algorithms are easy to implement and rely on a single projection per iteration. We prove several convergence results and establish rate of convergence estimates under various and mild assumptions on the problem's data and the corresponding step-sizes.}, identifier = {05550707}, }