Math 126 Winter 2018
Current Problems in Applied Mathematics: Convex Optimization
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Project
Student should choose a suitable paper by Feb 9 (F).
Written report (3-5 pages) is due by Mar 5 (M).
Oral presentation (20 minutes including questions): Mar 2 (F), Mar 5 (M)
The following is a sample list of recommeded topics and articles for the project.
H. H. Bauschke, J. Bolte, M. Teboulle,
A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications
, Mathematics of Operations Research, 2017
A. Beck, M. Teboulle,
Smoothing and First Order Methods: A Unified Framework
, SIAM Journal on Optimization, 2012
S. R. Becker, E. J. Candes, M. C. Grant,
Templates for Convex Cone Problems with Applications to Sparse Signal Recovery
, Mathematical Programming Computation, 2011
N. Boyd, G. Schiebinger, B. Recht,
The Alternating Descent Conditional Gradient Method for Sparse Inverse Problems
, SIAM Journal on Optimization, 2017
R. H. Byrd, S. L. Hansen, J. Nocedal, Y. Signer,
A Stochastic Quasi-Newton Method for Large-Scale Optimization
, SIAM Journal on Optimization, 2016
J.-F. Cai, E. J. Candes, Z. Shen,
A Singular Value Thresholding Algorithm for Matrix Completion
, SIAM Journal on Optimization,2010
E. J. Candes, Y. C. Eldar, T. Strohmer, V. Voroninski,
Phase Retrieval via Matrix Completion
, SIAM Journal on Imaging Sciences, 2013
Y. Drori, M. Teboulle,
Performance of First-order Methods for Smooth Convex Minimization: A Novel Approach
, Mathematical Programming, 2014
O. Fercoq, P. Richtarik,
Accelerated, Parallel, and Proximal Coordinate Descent
, SIAM Journal on Optimization, 2015
T. Goldstein, B. O'Donoghue, S. Setzer, R. Baraniuk,
Fast Alternating Direction Optimization Methods
, SIAM Journal on Imaging Sciences, 2014
R. Madani, S. Sojoudi, G. Fazelnia, J. Lavaei,
Finding Low-rank Solutions of Sparse Linear Matrix Inequalities using Convex Optimization
, SIAM J. Optimization, 2017
I. Necoara, Y. Nesterov, F. Glineur,
Linear Convergence of First Order Methods for Non-strongly Convex Optimization
, Mathematical Programming, 2018
Y. Nesterov, B. T. Polyak,
Cubic Regularization of Newton Method and Its Global Performance
, Mathematical Programming, 2006
B. O'Donoghue, E. J. Candes,
Adaptive Restart for Accelerated Gradient Schemes
, Foundations of Computational Mathematics, 2015
W. Su, S. Boyd, E. J. Candes,
A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights
, Journal of Machine Learning Research, 2016
A. C. Wilson, R. Roelofs, M. Stern, N. Srebro, B. Recht,
The Marginal Value of Adaptive Gradient Methods in Machine Learning
, Advances in Neural Information Processing Systems, 2017
S. J. Wright,
Coordinate Descent Algorithms
, Mathematical Programming, 2015
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