Complexity bounds for primal-dual methods minimizing the model of objective function

Yurii Nesterov ()
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Yurii Nesterov: Université catholique de Louvain, CORE, Belgium

No 2015003, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: We provide Frank-Wolfe (= Conditional Gradients) method with a convergence analysis allowing to approach a primal-dual solution of convex optimization problem with composite objective function. Additional properties of complementary part of the objective (strong convexity) significantly accelerate the scheme. We also justify a new variant of this method, which can be seen as a trust-region scheme applying the linear model of objective function. Our analysis works also for a quadratic model, allowing to justify the global rate of convergence for a new second-order method. To the best of our knowledge, this is the first trust-region scheme supported by the worst-case complexity bound.

Keywords: convex optimization; complexity bounds; linear optimization oracle; conditional gradient method; trust-region method (search for similar items in EconPapers)
Date: 2015-02-02
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Citations: View citations in EconPapers (15)

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