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AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
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WINE'07 Proceedings of the 3rd international conference on Internet and network economics
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ALT'11 Proceedings of the 22nd international conference on Algorithmic learning theory
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IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
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Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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AI Communications
Computational Optimization and Applications
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Accelerated training of max-margin Markov networks with kernels
Theoretical Computer Science
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International Journal of Bioinformatics Research and Applications
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In this paper we introduce a new primal-dual technique for convergence analysis of gradient schemes for nonsmooth convex optimization. As an example of its application, we derive a primal-dual gradient method for a special class of structured nonsmooth optimization problems, which ensures a rate of convergence of order O(1/k), where k is the iteration count. Another example is a gradient scheme, which minimizes a nonsmooth strongly convex function with known structure with rate of convergence O(1/k2). In both cases the efficiency of the methods is higher than the corresponding black-box lower complexity bounds by an order of magnitude.