, Matthieu Devin, and others. Tensorflow: Large-scale machine learning on heterogeneous distributed systems, 2016.

A learning algorithm for Boltzmann machines, Cognitive science, vol.9, issue.1, pp.147-169, 1985. ,

Almost everywhere existence of the second differential of a convex function and some properties of convex functions, Leningrad Univ. Ann, vol.37, pp.3-35, 1939. ,

Convex multitask feature learning, Machine Learning, vol.73, pp.243-272, 2008. ,

Consistency of trace norm minimization, Journal of Machine Learning Research, vol.9, pp.1019-1048, 2008. ,

URL : https://hal.archives-ouvertes.fr/hal-00179522

On the low-rank approach for semidefinite programs arising in synchronization and community detection, 2016. ,

Linearly convergent away-step conditional gradient for non-strongly convex functions, Mathematical Programming, pp.1-27, 2015. ,

A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM journal on imaging sciences, vol.2, issue.1, pp.183-202, 2009. ,

Distributed Frank-Wolfe algorithm: A unified framework for communication-efficient sparse learning. CoRR, abs/1404.2644, 2014. ,

Global optimality of local search for low rank matrix recovery, Advances in Neural Information Processing Systems, pp.3873-3881, 2016. ,

, Pattern recognition. Machine Learning, vol.128, pp.1-58, 2006.

Convex optimization, 2004. ,

, Krümmungseigenschaften konvexer Flächen. Acta Mathematica, vol.66, issue.1, pp.1-47, 1936.

Unifying Nuclear Norm and Bilinear Factorization Approaches for Low-Rank Matrix Decomposition, 2013 IEEE International Conference on Computer Vision, pp.2488-2495, 2013. ,

Matrix Completion for Multi-label Image Classification, Advances in Neural Information Processing Systems, vol.24, pp.190-198, 2011. ,

A singular value thresholding algorithm for matrix completion, SIAM Journal on Optimization, vol.20, issue.4, pp.1956-1982, 2010. ,

Phase Retrieval via Matrix Completion, SIAM Journal on Imaging Sciences, vol.6, issue.1, pp.199-225, 2013. ,

Exact matrix completion via convex optimization, Communications of the ACM, vol.55, issue.6, pp.111-119, 2012. ,

Matrix completion with noise, Proceedings of the IEEE, vol.98, issue.6, pp.925-936, 2010. ,

The power of convex relaxation: Nearoptimal matrix completion, IEEE Transactions on Information Theory, vol.56, issue.5, pp.2053-2080, 2010. ,

Multitask learning, Learning to learn, pp.95-133, 1998. ,

The convex algebraic geometry of linear inverse problems, Communication, Control, and Computing (Allerton), 2010 48th Annual Allerton Conference on, pp.699-703, 2010. ,

Coherent Matrix Completion, PMLR, pp.674-682, 2014. ,

, , 2015.

Coresets, sparse greedy approximation, and the Frank-Wolfe algorithm, ACM Transactions on Algorithms (TALG), vol.6, issue.4, p.63, 2010. ,

Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids, Optimisation Methods and Software, vol.23, issue.1, pp.5-19, 2008. ,

Generalized iterative scaling for log-linear models. The annals of mathematical statistics, pp.1470-1480, 1972. ,

Smooth optimization with approximate gradient, SIAM Journal on Optimization, vol.19, issue.3, pp.1171-1183, 2008. ,

MapReduce: simplified data processing on large clusters, Communications of the ACM, vol.51, issue.1, pp.107-113, 2008. ,

Approximate methods in optimization problems, vol.32, 1970. ,

Imagenet: A large-scale hierarchical image database, Computer Vision and Pattern Recognition, pp.248-255, 2009. ,

Analysis of longitudinal data, 2002. ,

Learning low-rank output kernels, PMLR, pp.181-196, 2011. ,

Lifted coordinate descent for learning with trace-norm regularization, Artificial Intelligence and Statistics, pp.327-336, 2012. ,

URL : https://hal.archives-ouvertes.fr/hal-00756802

Rates of convergence for conditional gradient algorithms near singular and nonsingular extremals, SIAM Journal on Control and Optimization, vol.17, issue.2, pp.187-211, 1979. ,

Regularized multi-task learning, Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining, pp.109-117, 2004. ,

Rank minimization and applications in system theory, Proceedings of the 2004 American Control Conference, vol.4, pp.3273-3278, 2004. ,

A rank minimization heuristic with application to minimum order system approximation, American Control Conference, vol.6, pp.4734-4739, 2001. ,

Geometric measure theory, 2014. ,

An algorithm for quadratic programming, Naval Research Logistics Quarterly, vol.3, issue.1-2, pp.95-110, 1956. ,

New analysis and results for the Frank-Wolfe method, Mathematical Programming, vol.155, issue.1-2, pp.199-230, 2016. ,

An Extended Frank-Wolfe Method with "In-Face" Directions, and Its Application to Low-Rank Matrix Completion, SIAM Journal on Optimization, vol.27, issue.1, pp.319-346, 2017. ,

A modified Frank-Wolfe algorithm for solving the traffic assignment problem, Transportation Research Part B: Methodological, vol.18, issue.2, pp.169-177, 1984. ,

Faster Projection-free Convex Optimization over the Spectrahedron, Advances in Neural Information Processing Systems, pp.874-882, 2016. ,

Projection-free Algorithms for Convex Optimization and Online Learning, 2016. ,

A linearly convergent conditional gradient algorithm with applications to online and stochastic optimization, 2013. ,

Playing non-linear games with linear oracles, Foundations of Computer Science (FOCS), 2013 IEEE 54th Annual Symposium on, pp.420-428, 2013. ,

Faster Rates for the Frank-Wolfe Method over StronglyConvex Sets, PMLR, pp.541-549, 2015. ,

Online Learning of Eigenvectors, PMLR, pp.560-568, 2015. ,

Modern Real Analysis, 1995. ,

Escaping From Saddle PointsOnline Stochastic Gradient for Tensor Decomposition, 2015. ,

Matrix completion has no spurious local minimum, Advances in Neural Information Processing Systems, pp.2973-2981, 2016. ,

, , 2016.

Optimizing over the growing spectrahedron, Algorithms-ESA, pp.503-514, 2012. ,

Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming, Journal of the ACM (JACM), vol.42, issue.6, pp.1115-1145, 1995. ,

Transduction with Matrix Completion: Three Birds with One Stone, Advances in Neural Information Processing Systems 23, pp.757-765, 2010. ,

Linear Convergence of Stochastic Frank Wolfe Variants, 2017. ,

Trace lasso: a trace norm regularization for correlated designs, Advances in Neural Information Processing Systems, pp.2187-2195, 2011. ,

URL : https://hal.archives-ouvertes.fr/hal-00620197

Recovering low-rank matrices from few coefficients in any basis, IEEE Transactions on Information Theory, vol.57, issue.3, pp.1548-1566, 2011. ,

Quantum state tomography via compressed sensing, Physical review letters, vol.105, issue.15, p.150401, 2010. ,

Some comments on Wolfe's 'away step'. Mathematical Programming, vol.35, pp.110-119, 1986. ,

Large-scale image classification with trace-norm regularization, 2012 IEEE Conference on Computer Vision and Pattern Recognition, pp.3386-3393, 2012. ,

URL : https://hal.archives-ouvertes.fr/hal-00728388

Sparse approximate solutions to semidefinite programs, Latin American Symposium on Theoretical Informatics, pp.306-316, 2008. ,

Projection-free online learning, 2012. ,

Variance-reduced and projection-free stochastic optimization, International Conference on Machine Learning, pp.1263-1271, 2016. ,

, Elad Hazan and others. Introduction to online convex optimization. Foundations and Trends R in Optimization, vol.2, pp.157-325, 2016.

Deep residual learning for image recognition, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp.770-778, 2016. ,

Lectures on lipschitz analysis, 2005. ,

Matrix nearness problems and applications, 1988. ,

Robust and Effective Metric Learning Using Capped Trace Norm: Metric Learning via Capped Trace Norm, Proceedings of the 22Nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '16, pp.1605-1614, 2016. ,

Sparse convex optimization methods for machine learning, 2011. ,

Revisiting Frank-Wolfe: Projection-Free Sparse Convex Optimization, ICML 2013 -Proceedings of the 30th International Conference on Machine Learning, 2013. ,

A simple algorithm for nuclear norm regularized problems, Proceedings of the 27th International Conference on Machine Learning (ICML-10), pp.471-478, 2010. ,

Robust video denoising using low rank matrix completion, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.1791-1798, 2010. ,

An accelerated gradient method for trace norm minimization, Proceedings of the 26th annual international conference on machine learning, pp.457-464, 2009. ,

Accelerating stochastic gradient descent using predictive variance reduction, Advances in neural information processing systems, pp.315-323, 2013. ,

Rank selection in low-rank matrix approximations: A study of cross-validation for NMFs, Proc Conf Adv Neural Inf Process, vol.1, pp.10-15, 2010. ,

An interior-point method for large-scale l1-regularized logistic regression, Journal of Machine learning research, vol.8, pp.1519-1555, 2007. ,

Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion. The Annals of Statistics, pp.2302-2329, 2011. ,

URL : https://hal.archives-ouvertes.fr/hal-00676868

Matrix Factorization Techniques for Recommender Systems, Computer, vol.42, issue.8, pp.30-37, 2009. ,

Estimating the largest eigenvalue by the power and Lanczos algorithms with a random start, SIAM journal on matrix analysis and applications, vol.13, issue.4, pp.1094-1122, 1992. ,

A linearly convergent linear-time first-order algorithm for support vector classification with a core set result, INFORMS Journal on Computing, vol.23, issue.3, pp.377-391, 2011. ,

Graphchi: Large-scale graph computation on just a pc, 2012. ,

On the global linear convergence of Frank-Wolfe optimization variants, Advances in Neural Information Processing Systems, pp.496-504, 2015. ,

URL : https://hal.archives-ouvertes.fr/hal-01248675

Blockcoordinate Frank-Wolfe optimization for structural SVMs, 2012. ,

URL : https://hal.archives-ouvertes.fr/hal-00720158

Convergence analysis of a stochastic projection-free algorithm, stat, vol.1050, issue.5, 2015. ,

Joseph Louis) Lagrange. Mécanique analytique, 1811. ,

Random-effects models for longitudinal data, Biometrics, pp.963-974, 1982. ,

Conditional gradient sliding for convex optimization, SIAM Journal on Optimization, vol.26, issue.2, pp.1379-1409, 2016. ,

An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, 1950. ,

URL : https://hal.archives-ouvertes.fr/hal-01712947

Learning to learn with the informative vector machine, Proceedings of the twenty-first international conference on Machine learning, p.65, 2004. ,

Sur l'intégration des fonctions discontinues, 1910. ,

Improved efficiency of the Frank-Wolfe algorithm for convex network programs, Transportation Science, vol.19, issue.4, pp.445-462, 1985. ,

Practical large-scale optimization for max-norm regularization, Advances in Neural Information Processing Systems, pp.1297-1305, 2010. ,

, Constrained minimization methods. USSR Computational Mathematics and Mathematical Physics, vol.6, issue.5, pp.1-50, 1966.

Scaling Distributed Machine Learning with the Parameter Server, OSDI, vol.1, 2014. ,

Longitudinal data analysis using generalized linear models, Biometrika, pp.13-22, 1986. ,

Low-rank Similarity Metric Learning in High Dimensions, Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, AAAI'15, pp.2792-2799, 2015. ,

Approximate Conditional Gradient Descent on Multi-Class Classification, AAAI, pp.2301-2307, 2017. ,

A Unified Optimization View on Generalized Matching Pursuit and Frank-Wolfe, PMLR, pp.860-868, 2017. ,

Distributed GraphLab: a framework for machine learning and data mining in the cloud, Proceedings of the VLDB Endowment, vol.5, pp.716-727, 2012. ,

Fixed Point and Bregman Iterative Methods for Matrix Rank Minimization, 2009. ,

Mixed optimization for smooth functions, Advances in Neural Information Processing Systems, pp.674-682, 2013. ,

Optimization with first-order surrogate functions, Proceedings of the 30th International Conference on Machine Learning (ICML-13), pp.783-791, 2013. ,

URL : https://hal.archives-ouvertes.fr/hal-00822229

Pregel: a system for large-scale graph processing, Proceedings of the 2010 ACM SIGMOD International Conference on Management of data, pp.135-146, 2010. ,

A comparison of algorithms for maximum entropy parameter estimation, proceedings of the 6th conference on Natural language learning, vol.20, pp.1-7, 2002. ,

Probability of unique integer solution to a system of linear equations, European Journal of Operational Research, vol.214, issue.1, pp.27-30, 2011. ,

Efficient large-scale distributed training of conditional maximum entropy models, Advances in Neural Information Processing Systems, pp.1231-1239, 2009. ,

Linear regression under fixed-rank constraints: a Riemannian approach, Proceedings of the 28th international conference on machine learning, 2011. ,

Finding the point of a polyhedron closest to the origin, SIAM Journal on Control, vol.12, issue.1, pp.19-26, 1974. ,

Distributing frank-wolfe via map-reduce, ICDM, 2017. ,

Scalable Robust Matrix Recovery: Frank-Wolfe Meets Proximal Methods, SIAM Journal on Scientific Computing, vol.38, issue.5, pp.3291-3317, 2016. ,

, Introductory lectures on convex optimization: A basic course, vol.87, 2013.

, Yurii Nesterov and others. Gradient methods for minimizing composite objective function. Core Louvain-la-Neuve, 2007.

Fast stochastic Frank-Wolfe algorithms for nonlinear SVMs, Proceedings of the 2010 SIAM International Conference on Data Mining, pp.245-256, 2010. ,

Polytope conditioning and linear convergence of the Frank-Wolfe algorithm, 2015. ,

On the von Neumann and Frank-Wolfe Algorithms with Away Steps, SIAM Journal on Optimization, vol.26, issue.1, pp.499-512, 2016. ,

A survey of methods for distributed machine learning, Progress in Artificial Intelligence, vol.2, issue.1, pp.1-11, 2013. ,

Learning Infinite RBMs with Frank-Wolfe, Advances in Neural Information Processing Systems, pp.3063-3071, 2016. ,

Trace norm regularization: Reformulations, algorithms, and multi-task learning, SIAM Journal on Optimization, vol.20, issue.6, pp.3465-3489, 2010. ,

A simpler approach to matrix completion, Journal of Machine Learning Research, vol.12, pp.3413-3430, 2011. ,

Generalized equations and their solutions, Part II: Applications to nonlinear programming. Optimality and Stability in Mathematical Programming, pp.200-221, 1982. ,

, Convex analysis, 2015.

Principles of mathematical analysis, vol.3, 1964. ,

ImageNet Large Scale Visual Recognition Challenge, International Journal of Computer Vision (IJCV), vol.115, issue.3, pp.211-252, 2015. ,

Applied longitudinal data analysis: Modeling change and event occurrence, 2003. ,

Maximummargin matrix factorization, Advances in neural information processing systems, pp.1329-1336, 2005. ,

Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization methods and software, vol.11, pp.625-653, 1999. ,

When Are Nonconvex Problems Not Scary?, 2015. ,

Cambridge University Press, vol.63, pp.9-16, 1996. ,

Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society. Series B (Methodological), pp.267-288, 1996. ,

An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems, Pacific Journal of optimization, vol.6, p.15, 2010. ,

SDPT3-a MATLAB software package for semidefinite programming, version 1.3. Optimization methods and software, vol.11, pp.545-581, 1999. ,

Distributed asynchronous deterministic and stochastic gradient optimization algorithms, IEEE transactions on automatic control, vol.31, issue.9, pp.803-812, 1986. ,

Low-rank matrix completion by Riemannian optimization, SIAM Journal on Optimization, vol.23, issue.2, pp.1214-1236, 2013. ,

Decentralized FrankWolfe Algorithm for Convex and Non-convex Problems, IEEE Transactions on Automatic Control, 2017. ,

Fast and privacy preserving distributed low-rank regression, Acoustics, Speech and Signal Processing (ICASSP, pp.4451-4455, 2017. ,

URL : https://hal.archives-ouvertes.fr/hal-01668252

Suvrit Sra, and Eric Xing. Parallel and distributed block-coordinate Frank-Wolfe algorithms, International Conference on Machine Learning, pp.1548-1557, 2016. ,

Convergence theory in nonlinear programming. Integer and nonlinear programming, pp.1-36, 1970. ,

Petuum: A new platform for distributed machine learning on big data, IEEE Transactions on Big Data, vol.1, issue.2, pp.49-67, 2015. ,

, Strategies and Principles of Distributed Machine Learning on Big Data, 2015.

, Convergence Analysis of the Frank-Wolfe Algorithm and Its Generalization in Banach Spaces, 2017.

Metric learning with trace-norm regularization for person re-identification, 2014 IEEE International Conference on Image Processing (ICIP), pp.2442-2446, 2014. ,

Dual coordinate descent methods for logistic regression and maximum entropy models, Machine Learning, vol.85, pp.41-75, 2011. ,

Fast and interactive analytics over Hadoop data with Spark, USENIX Login, vol.37, issue.4, pp.45-51, 2012. ,

Resilient distributed datasets: A fault-tolerant abstraction for in-memory cluster computing, Proceedings of the 9th USENIX conference on Networked Systems Design and Implementation, pp.2-2, 2012. ,

Longitudinal data analysis for discrete and continuous outcomes, Biometrics, pp.121-130, 1986. ,

MALSAR: Multi-tAsk Learning via StructurAl Regularization, 2011. ,

A multi-task learning formulation for predicting disease progression, Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining, pp.814-822 ,

Multi-task learning: Theory, algorithms, and applications, 2012. ,

Infinite latent SVM for classification and multi-task learning, Advances in neural information processing systems, pp.1620-1628, 2011. ,

Parallelized stochastic gradient descent, Advances in neural information processing systems, pp.2595-2603, 2010. ,

A novel Frank-Wolfe algorithm. Analysis and applications to large-scale SVM training, Information Sciences, vol.285, pp.66-99, 2014. ,