- First homework, due Mar 11
- Second homework, due April 11

**Week 1:****Basic continuous optimization**(descent directions, coordinate ascent, EM as coordinate ascent, Newton's method, stabilized Newton's method);**Week 2, Week 3:**More basic continuous optimization (trust regions, dogleg method, subspace method); My notes: (Conjugate gradient); (Conjugate gradient and Polak Ribiere Notes); My notes (Quasi Newton methods for big problems, including DFP, BFGS, limited memory methods) My notes:- Week 4, 5 and 6: Constrained optimization methods
- Lagrangians, quadratic penalty method, augmented lagrangian method (My notes:)
- Linear programs as an example (My notes)
- Inequality constraints in Lagrangians and KKT; relations between primal and dual (My notes)
- Active set methods and box constraints (my notes)
- Logistic regression as a classifier
**(**my notes) - The SVM as an example (My notes)
- Stochastic gradient descent (my notes)
- Semi-definite programs (My notes - these really do start at page 5!)
- Interior point methods (My notes); merit functions and the Maratos effect (my notes)
- L1 logistic regression, homotopy paths, subgradients and pursuit methods (my notes)
- Quadratic programming and sequential quadratic programming (my notes)
- Gradient Boost (my notes)
- Initial remarks on Combinatorial optimization (my notes); Flow and cuts (my notes)
**alpha-expansion, alpha-beta swaps; MRF's as cuts**(my notes):**Stochastic Average Gradient**(my notes)- Matchings (my notes);
**bipartite graph matching as a linear program**(my notes) **Dual decomposition methods**(my notes);**ADMM**(my notes there really are two page 13's, sorry)**ADMM for discrete problems**(my notes)

- Numerical Optimization (Springer Series in Operations Research and Financial Engineering) by Jorge Nocedal and Stephen Wright, 2006
- Convex Optimization by Stephen Boyd and Lieven Vandenberghe, Cambridge, 2004
- Understanding and Using Linear Programming, J. Matousek and B. Gartner, Springer, 2007
- Introduction to Optimization, P. Pedregal, Springer, 2004
- Optimization for Machine Learning, Sra, Nowozin and Wright, MIT Press, 2011
- Foundations of Optimization, Guler, Springer, 2010
- Nonlinear Programming by Dimitri P. Bertsekas, Athena, 1999
- Practical Methods of Optimization by R. Fletcher, Wiley, 2000
- Practical Optimization by Philip E. Gill, Walter Murray, Margaret H. Wright, Academic, 1982

Useful papers

- Johathan Shewchuk, An Introduction to the conjugate gradient method without the agonizing pain, 1994
- F.A. Potra, S.J. Wright, "Interior point methods", Journal of Computational and Applied Mathematics

Volume 124, Issues 1-2, 1 December 2000, Pages 281-302 (find it here from a computer inside UIUC VPN) - S. Shalev-Shwartz and Y. Singer, "Logarithmic regret algorithms for strongly convex repeated games", TR, Hebrew University, 2007

**Decomposition**

- S. Boyd, L. Xiao, A. Mutapcic, J. Mattingley, Notes on Decomposition methods, 2008
- Alexander M. Rush and Michael Collins. A tutorial on Lagrangian relaxation and dual decomposition for NLP.

In Journal of Artificial Intelligence Research, 2012 - Introduction to Dual Decomposition for Inference David Sontag, Amir Globerson and Tommi Jaakkola

Book chapter in Optimization for Machine Learning, editors S. Sra, S. Nowozin, and S. J. Wright: MIT Press, 2011 .

**Alternating Direction Method of Multipliers**

- Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein

Foundations and Trends in Machine Learning, 3(1):1–122, 2011. - André F. T. Martins, Mário A. T. Figueiredo, Pedro M. Q. Aguiar, Noah A. Smith, and Eric P. Xing.

"An Augmented Lagrangian Approach to Constrained MAP Inference."

International Conference on Machine Learning (ICML'11), Bellevue, Washington, USA, June 2011. - André F. T. Martins, Noah A. Smith, Mário A. T. Figueiredo, Pedro M. Q. Aguiar.

"Dual Decomposition With Many Overlapping Components."

Empirical Methods in Natural Language Processing (EMNLP'11), Edinburgh, UK, July 2011. - Efficient projections onto the l 1-ball for learning in high dimensions, John Duchi, Shai Shalev-Shwartz, Yoram Singer, Tushar Chandra, Proceedings of the 25th international conference on Machine learning, 2008

L1 Logistic Regression and regularization paths

- J. Mairal, B. Yu. Complexity Analysis of the Lasso Regularization Path. International Conference on Machine Learning, 2012
- Osborne, M., Presnell, B., and Turlach, B. A new approach to variable selection in least squares prob- lems. IMA J. Numer. Anal., 20(3):389–403, 2000
- Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani, Least Angle Regression Annals of Statistics (with discussion) (2004) 32(2), 407-499.
- Trevor Hastie, Saharon Rosset, Rob Tibshirani and Ji Zhu, The Entire Regularization Path for the Support Vector Machine, NIPS 2004

**Gradient Boost**

- Jerome H. Friedman, Greedy Function Approximation: A Gradient Boosting Machine , The Annals of Statistics, Vol. 29, No. 5 (Oct., 2001), pp. 1189-1232

Neat MRF algorithm cheat-sheet

- Which Energy Minimization for my MRF/CRF? A Cheat-Sheet, Bogdan Alexe, Thomas Deselaers, Marcin Eicher, Vittorio Ferrari, Peter Gehler, Alain Lehmann, Stefano Pellegrini, Alessandro Prest

- Submodular function tutorial slides (Krause, Guestrin, 2008)
- Batch Mode Active Learning and Its Application to Medical Image Classification, Hoi, Jin, Zhu and Lyu, ICML 08

- An Introduction to Bilevel Programming (Fricke, ND)
- Classfication model selection via bilevel programming, Kunapuli, Bennet, Hu and Pang, Optimization Methods and Software, 2008

## Continuous optimization applications

- The improved
iterative scaling algorithm: A gentle introduction

A Berger - Unpublished manuscript, 1997 - Iain Bancarz, M. Osborne, Improved iterative scaling can
yield multiple globally optimal models with radically differing
performance levels, Proceedings of the 19th international
conference on Computational linguistics, 1 - 7, 2002

- Robert Malouf, A
comparison of algorithms for maximum entropy parameter estimation,

proceeding of the 6th conference on Natural language learning - Volume 20, 1 - 7, 2002 - F. Sha and F. Pereira, Shallow parsing with conditional random fields, Proc HLT-NAACL, Main papers, pp 134-141, 2003
- Hanna Wallach, Efficient Training of Conditional Random Fields, University of Edinburgh, 2002.

- Jerome H. Friedman, Greedy Function Approximation: A Gradient Boosting Machine , The Annals of Statistics, Vol. 29, No. 5 (Oct., 2001), pp. 1189-1232

- Bill Triggs, Philip F. McLauchlan,
Richard I. Hartley and Andrew W. Fitzgibbon, Bundle Adjustment -- A Modern
Synthesis,
Vision Algorithms: Theory and Practice: International Workshop on
Vision Algorithms, Corfu, Greece, September 1999, pp153-177,

- Buchanan, A.M.; Fitzgibbon, A.W., Damped Newton algorithms for matrix factorization with missing data, Computer Vision and Pattern Recognition, 2005, 316 - 322
- Fast Maximum Margin Matrix Factorization for Collaborative Prediction, Jason D. M. Rennie, Nati Srebro, in Luc De Raedt, Stefan Wrobel (Eds.) Proceedings of the 22nd International Machine Learning Conference, ACM Press, 2005
- Scene Discovery by Matrix Factorization, N.Loeff, A. Farhadi, ECCV 2008
- T. Finley and T.Joachims, Supervised clustering with support vector machines, Proceedings of the 22nd international conference on Machine learning, 217 - 224, 2005

- A.W. Fitzgibbon, Robust registration of 2D and 3D point sets, Image and Vision Computing, Volume 21, Issues 13-14, 1 December 2003, Pages 1145-1153

- C.J.C. Burges, ``A Tutorial on Support Vector Machines for Pattern Recognition, '' Data Mining and Knowledge Discovery, 2, 121-167 (1998)
- Sequential minimal optimization: A fast algorithm for training support vector machines J Platt - Advances in Kernel Methods-Support Vector Learning, 1999
- S. S. Keerthi, S. K. Shevade,C. Bhattacharyya, K. R. K. Murthy, Improvements to Platt's SMO Algorithm for SVM Classifier Design, Neural Computation. 2001;13:637-649, 2001
- Dynamic visual category learning, T.Yeh and T. Darrell, CVPR, 2008
- K. Zhang, I.W. Tsang, J.T. Kwok, Maximum margin clustering made practical, Proceedings of the 24th international conference on Machine learning, 1119 - 1126, 2007
- Pegasos: Primal Estimated sub-GrAdient SOlver for SVM, S. Shalev-Shwartz, Y. Singer, N. Srebro, ICML 2008

- I. Tsochantaridis, T. Joachims, T. Hofmann, and Y. Altun, Large Margin Methods for Structured and Interdependent Output Variables, Journal of Machine Learning Research (JMLR), 6(Sep):1453-1484, 2005.
- Subgradient Methods for Maximum Margin Structured Learning Nathan D. Ratliff J. Andrew Bagnell Martin A. Zinkevich
- Learning to localize objects with structured output regression, Blaschko and Lamport, ECCV 2008
- Smooth minimization of non-smooth functions (Nesterov; Math. Prog 2005).
- M. Goemans and D.P Williamson, Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming, Journal of the ACM, Volume 42 , Issue 6, 1115 - 1145, 1995
- L.Vandenberghe and S.Boyd, Semidefinite programming, SIAM review, 38, 1, 49-95, 1996
- A Tutorial on Dual Decomposition and Lagrangian Relaxation for Inference in Natural Language Processing, A.M. Rush and M. Collins, JMLR,

- Y Rubner, C Tomasi, LJ Guibas, The Earth Mover's Distance as a Metric for Image Retrieval, International Journal of Computer Vision, 2000
- Grauman, K. Darrell, T., Fast contour matching using approximate earth mover's distance. CVPR 2004
- E Levina, P Bickel, The earth mover’s distance is the Mallows distance: Some insights from statistics, Proc. ICCV, 2001
- S Belongie, J Malik, J Puzicha, Matching shapes, Proc. of ICCV, 2001
- Maciel, J.; Costeira, J.P.; A global solution to sparse correspondence problems, Pattern Analysis and Machine Intelligence, IEEE Transactions on, Volume 25, Issue 2, Feb. 2003 Page(s):187 - 19
- A.Berg, T. Berg and J. Malik, Shape matching and object recognition using low distortion correspondence, CVPR, 2005
- Boykov, Y. and O. Veksler, Graph cuts in vision and graphics: theories and applications, Handbook of Math. Models of Computer Vision, Paragios, Chen, Faugeras (eds)
- Boykov, Y. Veksler, O. Zabih, R. Fast approximate energy minimization via graph cuts, PAMI, 23, 11, 1222-1239, 2001
- Boykov, Y. Veksler, O. Zabih, R., Markov random fields with efficient approximations, CVPR, 1998
- P. Kohli and M. Pawan Kumar and P.H.S. Torr, P^3 and Beyond: Solving Energies with Higher Order Cliques, CVPR 2007
- C.Olsson A.P. Eriksson and F. Kahl, Solving Large Scale Binary Quadratic Problems: Spectral Methods vs Semidefinite Programming, CVPR 2007
- Accelerated dual decomposition for MAP inference (Jojic, Gould, Koller; ICML 2010).
- MRF Energy Minimization and Beyond via Dual Decomposition (Komodakis, Paragios; PAMI 2010)
- A Comparative Study of Energy Minimization Methods for Markov Random Fields, R. Szeliski, R. Zabih, D. Scharstein, O. Veksler, V. Kolmogorov, A. Agarwala, M.Tappen, and C. Rother, ECCV 2006
- Minimizing Nonsubmodular Functions with Graph Cuts—A Review, V. Kolmogorov and C. Rother, PAMI 2007
- Convergent Tree-Reweighted Message Passing for Energy Minimization, V. Kolmogorov, PAMI 2006
- Approximate labeling via graph cuts based on linear programming, N Komodakis… - Pattern Analysis and Machine Intelligence, 2007
- Dynamic graph cuts for efficient inference in markov random fields, P Kohli… - Pattern Analysis and Machine Intelligence,
2007
#### Submodular functions

- Kang, Jin, Sukthankar, Correlated label propagation with application to multi-label learning, CVPR 2006

## Discrete Optimization

## Resources

## Applications

## Matching

## Markov Random Fields