Approximate Level Method for Nonsmooth Convex Minimization

Peter Richtárik ()
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Peter Richtárik: University of Edinburgh

Journal of Optimization Theory and Applications, 2012, vol. 152, issue 2, No 3, 334-350

Abstract: Abstract In this paper, we propose and analyse an approximate variant of the level method of Lemaréchal, Nemirovskii and Nesterov for minimizing nonsmooth convex functions. The main per-iteration work of the level method is spent on (i) minimizing a piecewise-linear model of the objective function and (ii) projecting onto the intersection of the feasible region and a level set of the model function. We show that, by replacing exact computations in both cases by approximate computations, in relative scale, the theoretical iteration complexity increases only by a small factor which depends on the approximation level and reduces to one in the exact case.

Keywords: Level method; Approximate projections in relative scale; Nonsmooth convex minimization; Sensitivity analysis; Large-scale optimization (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-011-9908-1

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