Variational Analysis Perspective on Linear Convergence of Some First Order Methods for Nonsmooth Convex Optimization Problems
暂无分享,去创建一个
Jane J. Ye | Xiaoming Yuan | Shangzhi Zeng | Jin Zhang | Xiaoming Yuan | Shangzhi Zeng | Jin Zhang | J. Ye | X. Yuan
[1] Mark W. Schmidt,et al. Convergence Rates of Inexact Proximal-Gradient Methods for Convex Optimization , 2011, NIPS.
[2] Z. Luo,et al. On the Linear Convergence of a Proximal Gradient Method for a Class of Nonsmooth Convex Minimization Problems , 2013 .
[3] Shuzhong Zhang,et al. Global Error Bounds for Convex Conic Problems , 1998, SIAM J. Optim..
[4] Hui Zhang. New analysis of linear convergence of gradient-type methods via unifying error bound conditions , 2020, Math. Program..
[5] Helmut Gfrerer,et al. JOHANNES KEPLER UNIVERSITY LINZ Institute of Computational Mathematics On Directional Metric Regularity, Subregularity and Optimality Conditions for Nonsmooth Mathematical Programs , 2012 .
[6] Amir Beck,et al. First-Order Methods in Optimization , 2017 .
[7] Guoyin Li,et al. Calculus of the Exponent of Kurdyka–Łojasiewicz Inequality and Its Applications to Linear Convergence of First-Order Methods , 2016, Foundations of Computational Mathematics.
[8] Z.-Q. Luo,et al. Error bounds and convergence analysis of feasible descent methods: a general approach , 1993, Ann. Oper. Res..
[9] D. Russell Luke,et al. Quantitative Convergence Analysis of Iterated Expansive, Set-Valued Mappings , 2016, Math. Oper. Res..
[10] B. Martinet. Brève communication. Régularisation d'inéquations variationnelles par approximations successives , 1970 .
[11] Zhi-Quan Luo,et al. Iteration complexity analysis of block coordinate descent methods , 2013, Mathematical Programming.
[12] Diethard Klatte,et al. Error bounds for solutions of linear equations and inequalities , 1995, Math. Methods Oper. Res..
[13] René Henrion,et al. On the Calmness of a Class of Multifunctions , 2002, SIAM J. Optim..
[14] Chih-Jen Lin,et al. Iteration complexity of feasible descent methods for convex optimization , 2014, J. Mach. Learn. Res..
[15] Peter Richtárik,et al. Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function , 2011, Mathematical Programming.
[16] Bernhard Schölkopf,et al. Causal Discovery from Heterogeneous/Nonstationary Data , 2019, J. Mach. Learn. Res..
[17] Yurii Nesterov,et al. Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.
[18] Juan C. Vera,et al. An algorithm to compute the Hoffman constant of a system of linear constraints , 2018, 1804.08418.
[19] F. J. A. Artacho,et al. Characterization of Metric Regularity of Subdifferentials , 2008 .
[20] Jean-Pierre Aubin,et al. Lipschitz Behavior of Solutions to Convex Minimization Problems , 1984, Math. Oper. Res..
[21] Jane J. Ye,et al. Perturbation Techniques for Convergence Analysis of Proximal Gradient Method and Other First-Order Algorithms via Variational Analysis , 2018, Set-Valued and Variational Analysis.
[22] S. M. Robinson. Stability Theory for Systems of Inequalities, Part II: Differentiable Nonlinear Systems , 1976 .
[23] Ion Necoara,et al. Efficient parallel coordinate descent algorithm for convex optimization problems with separable constraints: Application to distributed MPC , 2013, 1302.3092.
[24] R. Tibshirani,et al. A note on the group lasso and a sparse group lasso , 2010, 1001.0736.
[25] S. M. Robinson. An Implicit-Function Theorem for Generalized Variational Inequalities. , 1976 .
[26] Diethard Klatte,et al. Constrained Minima and Lipschitzian Penalties in Metric Spaces , 2002, SIAM J. Optim..
[27] Yurii Nesterov,et al. Linear convergence of first order methods for non-strongly convex optimization , 2015, Math. Program..
[28] F. J. A. Artacho,et al. Metric subregularity of the convex subdifferential in Banach spaces , 2013, 1303.3654.
[29] Asen L. Dontchev,et al. Regularity and Conditioning of Solution Mappings in Variational Analysis , 2004 .
[30] F. Facchinei,et al. Finite-Dimensional Variational Inequalities and Complementarity Problems , 2003 .
[31] Nasser M. Nasrabadi,et al. Pattern Recognition and Machine Learning , 2006, Technometrics.
[32] Xi Yin Zheng,et al. Metric Subregularity of Piecewise Linear Multifunctions and Applications to Piecewise Linear Multiobjective Optimization , 2014, SIAM J. Optim..
[33] Martin J. Wainwright,et al. Fast global convergence of gradient methods for high-dimensional statistical recovery , 2011, ArXiv.
[34] Marc Teboulle,et al. A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..
[35] Marc Teboulle,et al. On the rate of convergence of the proximal alternating linearized minimization algorithm for convex problems , 2016, EURO J. Comput. Optim..
[36] M. Yuan,et al. Model selection and estimation in regression with grouped variables , 2006 .
[37] S. M. Robinson. Stability Theory for Systems of Inequalities. Part I: Linear Systems , 1975 .
[38] Yurii Nesterov,et al. Random Block Coordinate Descent Methods for Linearly Constrained Optimization over Networks , 2015, J. Optim. Theory Appl..
[39] Anthony Man-Cho So,et al. A unified approach to error bounds for structured convex optimization problems , 2015, Mathematical Programming.
[40] Peter Richtárik,et al. Optimization in High Dimensions via Accelerated, Parallel, and Proximal Coordinate Descent , 2016, SIAM Rev..
[41] Uriel G. Rothblum,et al. Approximations to Solutions to Systems of Linear Inequalities , 1995, SIAM J. Matrix Anal. Appl..
[42] Jane J. Ye,et al. Verifiable sufficient conditions for the error bound property of second-order cone complementarity problems , 2017, Mathematical Programming.
[43] Lei Guo,et al. Mathematical Programs with Geometric Constraints in Banach Spaces: Enhanced Optimality, Exact Penalty, and Sensitivity , 2013, SIAM J. Optim..
[44] Bruce W. Suter,et al. From error bounds to the complexity of first-order descent methods for convex functions , 2015, Math. Program..
[45] René Henrion,et al. Calmness of constraint systems with applications , 2005, Math. Program..
[46] P. Tseng,et al. On the linear convergence of descent methods for convex essentially smooth minimization , 1992 .
[47] Tuo Zhao,et al. An Improved Convergence Analysis of Cyclic Block Coordinate Descent-type Methods for Strongly Convex Minimization , 2016, AISTATS.
[48] Qi Zhang,et al. \(\ell_{1, p}\)-Norm Regularization: Error Bounds and Convergence Rate Analysis of First-Order Methods , 2015, ICML.
[49] R. Tibshirani. Regression Shrinkage and Selection via the Lasso , 1996 .
[50] Stephen P. Boyd,et al. Enhancing Sparsity by Reweighted ℓ1 Minimization , 2007, 0711.1612.
[51] Paul Tseng,et al. Approximation accuracy, gradient methods, and error bound for structured convex optimization , 2010, Math. Program..
[52] Dmitriy Drusvyatskiy,et al. Error Bounds, Quadratic Growth, and Linear Convergence of Proximal Methods , 2016, Math. Oper. Res..
[53] Marc Teboulle,et al. Proximal alternating linearized minimization for nonconvex and nonsmooth problems , 2013, Mathematical Programming.
[54] A. Hoffman. On approximate solutions of systems of linear inequalities , 1952 .
[55] Luis Zuluaga,et al. New characterizations of Hoffman constants for systems of linear constraints , 2019, Mathematical Programming.
[56] J. J. Ye,et al. Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints , 1997, Math. Oper. Res..
[57] Lin Xiao,et al. A Proximal-Gradient Homotopy Method for the Sparse Least-Squares Problem , 2012, SIAM J. Optim..
[58] Julien Mairal,et al. Optimization with Sparsity-Inducing Penalties , 2011, Found. Trends Mach. Learn..
[59] Shaohua Pan,et al. Several Classes of Stationary Points for Rank Regularized Minimization Problems , 2019, SIAM J. Optim..
[60] Mark W. Schmidt,et al. Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Łojasiewicz Condition , 2016, ECML/PKDD.
[61] R. Tibshirani,et al. Sparsity and smoothness via the fused lasso , 2005 .
[62] S. M. Robinson. Some continuity properties of polyhedral multifunctions , 1981 .
[63] Emmanuel J. Candès,et al. Adaptive Restart for Accelerated Gradient Schemes , 2012, Foundations of Computational Mathematics.
[64] Ion Necoara,et al. Parallel Random Coordinate Descent Method for Composite Minimization: Convergence Analysis and Error Bounds , 2016, SIAM J. Optim..
[65] Jin Zhang,et al. Discerning the Linear Convergence of ADMM for Structured Convex Optimization through the Lens of Variational Analysis , 2020, J. Mach. Learn. Res..
[66] Helmut Gfrerer,et al. New Constraint Qualifications for Mathematical Programs with Equilibrium Constraints via Variational Analysis , 2022 .
[67] J. Stoer,et al. Convexity and Optimization in Finite Dimensions I , 1970 .
[68] HongMingyi,et al. Iteration complexity analysis of block coordinate descent methods , 2017 .
[69] H. Bondell,et al. Simultaneous Regression Shrinkage, Variable Selection, and Supervised Clustering of Predictors with OSCAR , 2008, Biometrics.
[70] Boris Polyak,et al. B.S. Mordukhovich. Variational Analysis and Generalized Differentiation. I. Basic Theory, II. Applications , 2009 .
[71] Paul Tseng,et al. A coordinate gradient descent method for nonsmooth separable minimization , 2008, Math. Program..
[72] Yurii Nesterov,et al. Efficiency of Coordinate Descent Methods on Huge-Scale Optimization Problems , 2012, SIAM J. Optim..
[73] Gregory B. Passty. Ergodic convergence to a zero of the sum of monotone operators in Hilbert space , 1979 .