Current Problems in Applied Mathematics: Convex Optimization

- 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