Generalizing the Optimized Gradient Method for Smooth Convex Minimization

This paper generalizes the optimized gradient method (OGM) [Y. Drori and M. Teboulle, Math. Program., 145 (2014), pp. 451--482], [D. Kim and J. A. Fessler, Math. Program., 159 (2016), pp. 81--107],...

[1]  Arkadi S. Nemirovsky,et al.  Information-based complexity of linear operator equations , 1992, J. Complex..

[2]  Stephen P. Boyd,et al.  Graph Implementations for Nonsmooth Convex Programs , 2008, Recent Advances in Learning and Control.

[3]  Marc Teboulle,et al.  Performance of first-order methods for smooth convex minimization: a novel approach , 2012, Mathematical Programming.

[4]  A. Chambolle,et al.  On the Convergence of the Iterates of the “Fast Iterative Shrinkage/Thresholding Algorithm” , 2015, J. Optim. Theory Appl..

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

[6]  Jeffrey A. Fessler,et al.  Another Look at the Fast Iterative Shrinkage/Thresholding Algorithm (FISTA) , 2016, SIAM J. Optim..

[7]  Osman Güler,et al.  New Proximal Point Algorithms for Convex Minimization , 1992, SIAM J. Optim..

[8]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[9]  Donghwan Kim,et al.  Optimized first-order methods for smooth convex minimization , 2014, Mathematical Programming.

[10]  Yurii Nesterov,et al.  Double Smoothing Technique for Large-Scale Linearly Constrained Convex Optimization , 2012, SIAM J. Optim..

[11]  Yoel Drori,et al.  The exact information-based complexity of smooth convex minimization , 2016, J. Complex..

[12]  Y. Nesterov.  A method for unconstrained convex minimization problem with the rate of convergence o(1/k^2) , 1983 .

[13]  Jeffrey A. Fessler,et al.  On the Convergence Analysis of the Optimized Gradient Method , 2015, J. Optim. Theory Appl..

[14]  Jeffrey A. Fessler,et al.  Optimizing the Efficiency of First-Order Methods for Decreasing the Gradient of Smooth Convex Functions , 2018, Journal of Optimization Theory and Applications.

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

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

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

[18]  Adrien B. Taylor,et al.  Smooth strongly convex interpolation and exact worst-case performance of first-order methods , 2015, Mathematical Programming.

[19]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[20]  Adrien B. Taylor,et al.  Exact Worst-Case Performance of First-Order Methods for Composite Convex Optimization , 2015, SIAM J. Optim..

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

[22]  Adrien B. Taylor,et al.  Efficient first-order methods for convex minimization: a constructive approach , 2018, Mathematical Programming.

[23]  Jeffrey A. Fessler,et al.  An optimized first-order method for image restoration , 2015, 2015 IEEE International Conference on Image Processing (ICIP).

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

[25]  Etienne de Klerk,et al.  On the worst-case complexity of the gradient method with exact line search for smooth strongly convex functions , 2016, Optimization Letters.

[26]  Juan Peypouquet,et al.  Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity , 2018, Math. Program..

[27]  Renato D. C. Monteiro,et al.  An Accelerated Hybrid Proximal Extragradient Method for Convex Optimization and Its Implications to Second-Order Methods , 2013, SIAM J. Optim..

[28]  Marc Teboulle,et al.  An optimal variant of Kelley’s cutting-plane method , 2014, Math. Program..

[29]  Saeed Ghadimi,et al.  Accelerated gradient methods for nonconvex nonlinear and stochastic programming , 2013, Mathematical Programming.

[30]  Boris Polyak.  Some methods of speeding up the convergence of iteration methods , 1964 .