In this paper we analyze the randomized block-coordinate descent (RBCD) methods for minimizing the sum of a smooth convex function and a block-separable convex function. In particular, we extend Nesterov’s technique (SIOPT 2012) for analyzing the RBCD method for minimizing a smooth convex function over a block-separable closed convex set to the aforementioned more general … Read more
In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an $\epsilon$-accurate solution with probability at least $1-\rho$ in at most $O(\tfrac{n}{\epsilon} \log \tfrac{1}{\rho})$ iterations, where $n$ is the number of blocks. For strongly convex functions … Read more
In this paper, we show that for a large class of optimization problems, the Lagrange multiplier rule can be derived from the so-called approximate multiplier rule. In establishing the link between the approximate and the exact multiplier rule we first derive an approximate multiplier rule for a very general class of optimization problems using the … Read more
Identification of active constraints in constrained optimization is of interest from both practical and theoretical viewpoints, as it holds the promise of reducing an inequality-constrained problem to an equality-constrained problem, in a neighborhood of a solution. We study this issue in the more general setting of composite nonsmooth minimization, in which the objective is a … Read more