Asymptotic convergence to the optimal value of diagonal proximal iterations in convex minimization

Given an approximation $\{f_n\}$ of a given objective function $f$, we provide simple and fairly general conditions under which a diagonal proximal point algorithm approximates the value $\inf f$ at a reasonable rate. We also perform some numerical tests and present a short survey on finite convergence.


To appear in Journal of Convex Analysis, 16 (2009), No 2.