Bundle-level type methods uniformly optimal for smooth and nonsmooth convex optimization
نویسندگان
چکیده
منابع مشابه
Bundle-level type methods uniformly optimal for smooth and nonsmooth convex optimization
The main goal of this paper is to develop uniformly optimal first-order methods for convex programming (CP). By uniform optimality we mean that the first-order methods themselves do not require the input of any problem parameters, but can still achieve the best possible iteration complexity bounds. By incorporating a multi-step acceleration scheme into the well-known bundle-level method, we dev...
متن کاملBundle-type methods uniformly optimal for smooth and nonsmooth convex optimization
The bundle-level method and its certain variants are known to exhibit an optimal rate of convergence, i.e., O(1/ √ t), and also excellent practical performance for solving general non-smooth convex programming (CP) problems. However, this rate of convergence is significantly worse than the optimal one for solving smooth CP problems, i.e., O(1/t). In this paper, we present new bundle-type method...
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The main goal of this paper is to develop uniformly optimal first-order methods for large-scale convex programming (CP). By uniform optimality we mean that the first-order methods themselves do not require the input of any problem parameters, but can still achieve the best possible iteration complexity bounds. To this end, we provide a substantial generalization of the accelerated level method ...
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We propose restricted memory level bundle methods for minimizing constrained convex nonsmooth optimization problems whose objective and constraint functions are known through oracles (black-boxes) that might provide inexact information. Our approach is general and covers many instances of inexact oracles, such as upper, lower and on-demand accuracy oracles. We show that the proposed level bundl...
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For solving nonsmooth convex constrained optimization problems, we propose an algorithm which combines the ideas of the proximal bundle methods with the filter strategy for evaluating candidate points. The resulting algorithm inherits some attractive features from both approaches. On the one hand, it allows effective control of the size of quadratic programming subproblems via the compression a...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2013
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-013-0737-x