Incremental Constraint Projection-Proximal Methods for Nonsmooth Convex Optimization
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چکیده
We consider convex optimization problems with structures that are suitable for stochastic sampling. In particular, we focus on problems where the objective function is an expected value or is a sum of a large number of component functions, and the constraint set is the intersection of a large number of simpler sets. We propose an algorithmic framework for projection-proximal methods using random subgradient/function updates and random constraint updates, which contain as special cases several known algorithms as well as new algorithms. To analyze the convergence of these algorithms in a unified manner, we prove a general coupled convergence theorem. It states that the convergence is obtained from an interplay between two coupled processes: progress towards feasibility and progress towards optimality. Moreover, we consider a number of typical sampling/randomization schemes for the subgradients/component functions and the constraints, and analyze their performance using our unified convergence framework. Report LIDS-P-2907, July 2013 Massachusetts Institute of Technology, Cambridge, MA Laboratory for Information and Decision Systems
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تاریخ انتشار 2013