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

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  • NESTEROV, Yurii

    (Université catholique de Louvain, CORE, Belgium)

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.

Suggested Citation

  • NESTEROV, Yurii, 2015. "Complexity bounds for primal-dual methods minimizing the model of objective function," LIDAM Discussion Papers CORE 2015003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2015003
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    References listed on IDEAS

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    1. Fujita,Masahisa & Thisse,Jacques-François, 2013. "Economics of Agglomeration," Cambridge Books, Cambridge University Press, number 9781107001411, January.
    2. Hindriks, Jean & Myles, Gareth D., 2013. "Intermediate Public Economics," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262018691, December.
    3. Nigar Hashimzade & Jean Hindriks & Gareth D. Myles, 2006. "Solutions Manual to Accompany Intermediate Public Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582694, December.
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    Cited by:

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    2. Madani, M. & Van Vyve, M., 2015. "A MIP framework for non-convex uniform price day-ahead electricity auctions," LIDAM Discussion Papers CORE 2015017, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Mattéo Godin & Jean Hindriks, 2015. "A Review of critical issues on tax design and tax administration in a global economy and developing countries," BeFinD Working Papers 0107, University of Namur, Department of Economics.
    4. Jean Hindriks & Yukihiro Nishimura, 2017. "Equilibrium leadership in tax competition models with capital ownership: a rejoinder," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(2), pages 338-349, April.
    5. Queyranne, M. & Wolsey, L.A., 2015. "Tight MIP Formulations for Bounded Up/Down Times and Interval-Dependent Start-Ups," LIDAM Discussion Papers CORE 2015036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    11. Yukihiro Nishimura & Pierre Pestieau, 2016. "Efficient taxation with differential risks of dependence and mortality," Economics Bulletin, AccessEcon, vol. 36(1), pages 52-57.
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