Accelerated Algorithms for Unconstrained Convex Optimization

[1]  Huan Li,et al.  On the Complexity Analysis of the Primal Solutions for the Accelerated Randomized Dual Coordinate Ascent , 2018, J. Mach. Learn. Res..

[2]  Yin Tat Lee,et al.  Near-optimal method for highly smooth convex optimization , 2018, COLT.

[3]  Xiaoming Yuan,et al.  An alternating direction method of multipliers with a worst-case O(1/n2) convergence rate , 2018, Mathematics of Computation.

[4]  Zhouchen Lin,et al.  Accelerated Alternating Direction Method of Multipliers: An Optimal O(1 / K) Nonergodic Analysis , 2016, Journal of Scientific Computing.

[5]  Ion Necoara,et al.  Complexity of first-order inexact Lagrangian and penalty methods for conic convex programming , 2015, Optim. Methods Softw..

[6]  Y. Nesterov,et al.  Linear convergence of first order methods for non-strongly convex optimization , 2015, Math. Program..

[7]  Yi Zhou,et al.  An optimal randomized incremental gradient method , 2015, Mathematical Programming.

[8]  Zaïd Harchaoui,et al.  Catalyst Acceleration for First-order Convex Optimization: from Theory to Practice , 2017, J. Mach. Learn. Res..

[9]  Zhouchen Lin,et al.  Convergence Rates Analysis of The Quadratic Penalty Method and Its Applications to Decentralized Distributed Optimization , 2017, 1711.10802.

[10]  Yangyang Xu,et al.  Accelerated First-Order Primal-Dual Proximal Methods for Linearly Constrained Composite Convex Programming , 2016, SIAM J. Optim..

[11]  Stephen P. Boyd,et al.  Linear Convergence and Metric Selection for Douglas-Rachford Splitting and ADMM , 2014, IEEE Transactions on Automatic Control.

[12]  Zeyuan Allen Zhu,et al.  Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent , 2014, ITCS.

[13]  Antonin Chambolle,et al.  On the ergodic convergence rates of a first-order primal–dual algorithm , 2016, Math. Program..

[14]  Zeyuan Allen Zhu,et al.  Optimal Black-Box Reductions Between Optimization Objectives , 2016, NIPS.

[15]  Andre Wibisono,et al.  A variational perspective on accelerated methods in optimization , 2016, Proceedings of the National Academy of Sciences.

[16]  Shuicheng Yan,et al.  Fast Proximal Linearized Alternating Direction Method of Multiplier with Parallel Splitting , 2015, AAAI.

[17]  Mikael Johansson,et al.  Convergence Analysis of Approximate Primal Solutions in Dual First-Order Methods , 2015, SIAM J. Optim..

[18]  Stephen P. Boyd,et al.  A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights , 2014, J. Mach. Learn. Res..

[19]  Ion Necoara,et al.  Iteration complexity analysis of dual first-order methods for conic convex programming , 2014, Optim. Methods Softw..

[20]  Benjamin Recht,et al.  Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints , 2014, SIAM J. Optim..

[21]  Damek Davis,et al.  Convergence Rate Analysis of Several Splitting Schemes , 2014, 1406.4834.

[22]  Bingsheng He,et al.  On non-ergodic convergence rate of Douglas–Rachford alternating direction method of multipliers , 2014, Numerische Mathematik.

[23]  Francis R. Bach,et al.  From Averaging to Acceleration, There is Only a Step-size , 2015, COLT.

[24]  Elad Hazan,et al.  Faster Rates for the Frank-Wolfe Method over Strongly-Convex Sets , 2014, ICML.

[25]  Yunmei Chen,et al.  An Accelerated Linearized Alternating Direction Method of Multipliers , 2014, SIAM J. Imaging Sci..

[26]  Emmanuel J. Candès,et al.  Adaptive Restart for Accelerated Gradient Schemes , 2012, Foundations of Computational Mathematics.

[27]  Yurii Nesterov,et al.  First-order methods of smooth convex optimization with inexact oracle , 2013, Mathematical Programming.

[28]  Ion Necoara,et al.  Rate Analysis of Inexact Dual First-Order Methods Application to Dual Decomposition , 2014, IEEE Transactions on Automatic Control.

[29]  Marc Teboulle,et al.  Rate of Convergence Analysis of Decomposition Methods Based on the Proximal Method of Multipliers for Convex Minimization , 2014, SIAM J. Optim..

[30]  Zhixun Su,et al.  Linearized alternating direction method with parallel splitting and adaptive penalty for separable convex programs in machine learning , 2013, Machine Learning.

[31]  Yunmei Chen,et al.  Optimal Primal-Dual Methods for a Class of Saddle Point Problems , 2013, SIAM J. Optim..

[32]  Alberto Bemporad,et al.  An Accelerated Dual Gradient-Projection Algorithm for Embedded Linear Model Predictive Control , 2014, IEEE Transactions on Automatic Control.

[33]  Martin Jaggi,et al.  Revisiting Frank-Wolfe: Projection-Free Sparse Convex Optimization , 2013, ICML.

[34]  Renato D. C. Monteiro,et al.  Iteration-complexity of first-order penalty methods for convex programming , 2013, Math. Program..

[35]  G. Sapiro,et al.  A collaborative framework for 3D alignment and classification of heterogeneous subvolumes in cryo-electron tomography. , 2013, Journal of structural biology.

[36]  Yurii Nesterov,et al.  Gradient methods for minimizing composite functions , 2012, Mathematical Programming.

[37]  Xiangfeng Wang,et al.  The Linearized Alternating Direction Method of Multipliers for Dantzig Selector , 2012, SIAM J. Sci. Comput..

[38]  Bingsheng He,et al.  On the O(1/n) Convergence Rate of the Douglas-Rachford Alternating Direction Method , 2012, SIAM J. Numer. Anal..

[39]  Mark W. Schmidt,et al.  Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization , 2011, NIPS.

[40]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[41]  Julien Mairal,et al.  Convex optimization with sparsity-inducing norms , 2011 .

[42]  Antonin Chambolle,et al.  A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging , 2011, Journal of Mathematical Imaging and Vision.

[43]  Tony F. Chan,et al.  A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science , 2010, SIAM J. Imaging Sci..

[44]  Martin Jaggi,et al.  A Simple Algorithm for Nuclear Norm Regularized Problems , 2010, ICML.

[45]  Xi Chen,et al.  Graph-Structured Multi-task Regression and an Efficient Optimization Method for General Fused Lasso , 2010, ArXiv.

[46]  Mohamed-Jalal Fadili,et al.  Total Variation Projection With First Order Schemes , 2011, IEEE Transactions on Image Processing.

[47]  Daniel Cremers,et al.  An algorithm for minimizing the Mumford-Shah functional , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[48]  Jean-Philippe Vert,et al.  Group lasso with overlap and graph lasso , 2009, ICML '09.

[49]  M. Baes Estimate sequence methods: extensions and approximations , 2009 .

[50]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[51]  Yurii Nesterov,et al.  Accelerating the cubic regularization of Newton’s method on convex problems , 2005, Math. Program..

[52]  Yurii Nesterov,et al.  Cubic regularization of Newton method and its global performance , 2006, Math. Program..

[53]  Yurii Nesterov,et al.  Smooth minimization of non-smooth functions , 2005, Math. Program..

[54]  Yurii Nesterov,et al.  Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.

[55]  Bingsheng He,et al.  A new inexact alternating directions method for monotone variational inequalities , 2002, Math. Program..

[56]  Convergence rate results for a penalty function method , 1978 .

[57]  B. T. Polyak,et al.  The convergence rate of the penalty function method , 1971 .

[58]  D. Luenberger Convergence rate of a penalty-function scheme , 1971 .

[59]  Philip Wolfe,et al.  An algorithm for quadratic programming , 1956 .