Convex optimization in R

Journal of Statistical Software

Volumn 60, Issue 5, 2014, Pages

  Koenker, Roger ^a   Mizera, Ivan ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Convexity; Lasso; Linear programming; Optimization; Penalty methods; Quadratic programming; Quantile regression; Second order cone programming; Semidefinite programming; Shape constrained methods

Indexed keywords

EID: 84907494974     PISSN: 15487660     EISSN: None     Source Type: Journal    
DOI: 10.18637/jss.v060.i05     Document Type: Article

References (64)

1. Arnold TB (2013). hdlm: Fitting High Dimensional Linear Models. R package version 1. 2, URL http://CRAN. R-project. org/package=hdlm.
2. Bakin S (1999). Adaptive Regression and Model Selection in Data Mining Problems. Ph. D. thesis, ANU.
3. Barrodale I, Roberts FDK (1974). "Solution of an Overdetermined System of Equations in the 1 Norm". Communications of the ACM, 17, 319-320.
4. Becker S, Bobin J, Candés EJ (2011a). "NESTA: A Fast and Accurate First-Order Method for Sparse Recovery". SIAM Journal on Imaging Sciences, 4, 1-39.
5. Becker SR, Candés EJ, Grant MC (2011b). "Templates for Convex Cone Problems with Applications to Sparse Signal Recovery". Mathematical Programming Computation, 3, 165-218.
6. Belloni A, Chernozhukov V, Wang L (2011). "Square-Root Lasso: Pivotal Recovery of Sparse Signals via Conic Programming". Biometrika, 98, 791-806.
7. Berkelaar M, Eikland K, Notebaert P (2012). lp solve: Linear Programming System. Version 5. 5, URL http://lpsolve. sourceforge. net/5. 5/.
8. Berkelaar M, et al. (2014). lpSolve: Interface to lp solve to Solve Linear-Integer Program. R package version 5. 6. 10, URL http://CRAN. R-project. org/package=lpSolve.
9. Borchers B (1999). "CSDP, a C Library for Semidefinite Programming". Optimization Methods and Software, 11(1), 613-623.
10. Boyd S, Vandenberghe L (2004). Convex Optimization. Cambridge University Press.
11. Cai JF, Candés EJ, Shen Z (2010). "A Singular Value Thresholding Algorithm for Matrix Completion". SIAM Journal on Optimization, 20, 1956-1982.
12. Candes E, Tao T (2007). "The Dantzig Selector: Statistical Estimation When p is Much Larger Than n". The Annals of Statistics, 35, 2313-2351.
13. Cule M, Samworth R, Stewart M (2010). "Computing the Maximum Likelihood Estimator of a Multidimensional Log-Concave Density". Journal of the Royal Statistical Society B, 72, 545-600.
14. CVX Research, Inc (2012). "CVX: MATLAB Software for Disciplined Convex Programming, Version 2. 0". URL http://cvxr. com/cvx/.
15. Dantzig GB (1951). "Maximization of a Linear Function of Variables Subject to Linear Inequalities". In TC Koopmans (ed.), Activity Analysis of Production and Allocation. John Wiley & Sons.
16. Donoho D, Chen SS, Saunders M (1998). "Atomic Decomposition by Basis Pursuit". SIAM Journal of Scientific Computing, 20, 33-61.
17. Dümbgen L, Rúbach K (2009). "Maximum Likelihood Estimation of a Log-Concave Density: Basic Properties and Uniform Consistency". Bernoulli, 15, 40-68.
18. Efron B, Hastie T, Johnstone I, Tibshirani R (2004). "Least Angle Regression". The Annals of Statistics, 32, 407-499.
19. Feuerverger A, He Y, Khatri S (2012). "Statistical Significance of the Netix Challenge". Statistical Science, 27, 202-231.
20. Fiacco AV, McCormick GP (1968). Nonlinear Programming: Sequential Unconstrained Min-imization Techniques. Research Analysis Corp., McLean. Reprinted in SIAM Classics in Applied Mathematics, 1990.
21. Friberg HA (2014). Rmosek: The R-to-MOSEK Optimization Interface. R package version 1. 2. 5. 1, URL http://CRAN. R-project. org/package=Rmosek.
22. Frisch R (1956). "La Résolution des Problémes de Programme Linéaire par la Méthode du Potential Logarithmique". Cahiers du Séminaire d'Econometrie, 4, 7-20.
23. Gill PE, Murray W, Saunders MA, Tomlin JA, Wright MH (1986). "On Projected Newton Barrier Methods for Linear Programming and an Equivalence to Karmarkar's Projective Method". Mathematical Programming, 36(2), 183-209.
24. Good IJ (1971). "A Nonparametric Roughness Penalty for Probability Densities". Nature, 229, 29-30.
25. Groeneboom P, Jongbloed G, Wellner JA (2008). "The Support Reduction Algorithm for Computing Non-Parametric Function Estimates in Mixture Models". Scandinavian Journal of Statistics, 35, 385-399.
26. Gurobi Optimization, Inc (2014). Gurobi Optimizer Reference Manual. URL http://www. gurobi. com/.
27. Gutenbrunner C, Jureckova J (1992). "Regression Quantile and Regression Rank Score Process in the Linear Model and Derived Statistics". The Annals of Statistics, 20, 305-330.
28. Hothorn T (2014). "CRAN Task View: Machine Learning & Statistical Learning". Version 2014-08-30, URL http://CRAN. R-project. org/view=MachineLearning.
29. Huang H, Haaland P, Lu X, Liu Y, Marron JS (2013). DWD: DWD Implementation Based on A IPM SOCP Solver. R package version 0. 11, URL http://CRAN. R-project. org/package=DWD.
30. Huber PJ (2009). "On the Non-Optimality of Optimal Procedures". In Optimality: The Third Erich L. Lehmann Symposium, IMS Lecture Notes-Monograph Series, volume 57, pp. 31-46. Institute of Mathematical Statistics.
31. IBM (2009). User Manual for CPLEX. URL http://www. ibm. com/software/integration/optimization/cplex-optimizer/.
32. Kantorovich LV (1939). Mathematical Methods of Organizing and Planning Production. Leningrad State University Publishers. Translation in Management Science, 6, 366-422 (1960).
33. Karatzoglou A, Smola A, Hornik K, Zeileis A (2004). "kernlab-An S4 Package for Kernel Methods in R". Journal of Statistical Software, 11(9), 1-20. URL http://www. jstatsoft. org/v11/i09/.
34. Karlin S (1959). Mathematical Methods and Theory in Games, Programming, and Economics. Addison-Wesley, Reading.
35. Karmarkar NA (1984). "A New Polynomial-Time Algorithm for Linear Programming". Com-binatorica, 4, 373-395.
36. Khachiyan LG (1979)". A Polynomial Algorithm in Linear Programming". Soviet Mathematics Doklady, 20, 191-194.
37. Kiefer J, Wolfowitz J (1956). "Consistency of the Maximum Likelihood Estimator in the Presence of Infinitely Many Incidental Parameters". The Annals of Mathematical Statistics, 27, 887-906.
38. Koenker R (2005). Quantile Regression. Cambridge University Press.
39. Koenker R (2011). "Additive Models for Quantile Regression: Model Selection and Confidence Bandaids". Brazilian Journal of Probability and Statistics, 25, 239-262.
40. Koenker R (2013). quantreg: Quantile Regression. R package version 5. 05, URL http://CRAN. R-project. org/package=quantreg.
41. Koenker R (2014). REBayes: Empirical Bayes Estimation and Inference in R. R package version 0. 50, URL http://CRAN. R-project. org/package=REBayes.
42. Koenker R, Mizera I (2006). "Density Estimation by Total Variation Regularization". In V Nair (ed.), Advances in Statistical Modeling and Inference, Essays in Honor of Kjell A. Doksum. World Scientific, Singapore.
43. Koenker R, Mizera I (2010). "Quasi-Concave Density Estimation". The Annals of Statistics, 38(5), 2998-3027.
44. Koenker R, Mizera I (2014). "Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules". Journal of the American Statistical Association, 109(506), 674-685.
45. Koenker R, Ng P (2005). "A Frisch-Newton Algorithm for Sparse Quantile Regression". Acta Mathematicae Applicatae Sinica, 21, 225-236.
46. Laird N (1978). "Nonparametric Maximum Likelihood Estimation of a Mixing Distribution". Journal of the American Statistical Association, 73, 805-811.
47. Mehrotra S (1992). "On the Implementation of a Primal-Dual Interior Point Method". SIAM Journal of Optimization, 2, 575-601.
48. Mittleman H (2012). "Mixed Integer Linear Programming Benchmark". URL http://plato. asu. edu/ftp/milpc. html.
49. MOSEK ApS, Denmark (2011). The MOSEK Optimization Tools Manual. Version 6. 0, URL http://www. mosek. com/.
50. Nesterov Y, Nemirovskii A (1987). Interior Point Polynomial Algorithms in Convex Program-ming. Society for Industrial and Applied Mathematics.
51. Portnoy S, Koenker R (1997). "The Gaussian Hare and the Laplacian Tortoise: Computability of Squared-Error Versus Absolute-Error Estimators". Statistical Science, 12, 279-300.
52. R Core Team (2014). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www. R-project. org/.
53. Rockafellar RT (1974). Conjugate Duality and Optimization. SIAM, Philadelphia.
54. Rockafellar RT (1996). Convex Analysis. Princeton University Press, Princeton.
55. Rockafellar T (1993). "Lagrange Multipliers and Optimality". SIAM Review, 35, 183-238.
56. Seregin A, Wellner JA (2010). "Nonparametric Estimation of Multivariate Convex-Transformed Densities". The Annals of Statistics, 38, 3751-3781.
57. Silverman BW(1982). "On the Estimation of a Probability Density Function by the Maximum Penalized Likelihood Method". The Annals of Statistics, 10, 795-810.
58. Theussl S (2014). "CRAN Task View: Optimization and Mathematical Programming". Version 2014-08-08, URL http://CRAN. R-project. org/view=Optimization.
59. Tibshirani R (1996). "Regression Shrinkage and Selection via the Lasso". Journal of the Royal Statistical Society B, 58, 267-288.
60. Toh KC, Todd MJ, Tutuncu RH (1999). "SDPT3-A MATLAB Software Package for Semidefinite Programming". Optimization Methods and Software, 11, 545-581.
61. Turlach BA, Weingessel A (2013). Quadprog: Functions to Solve Quadratic Program-ming Problems. R package version 1. 5-5, URL http://CRAN. R-project. org/package= quadprog.
62. Vapnik VN (2000). The Nature of Statistical Learning Theory. 2nd edition. Springer-Verlag, New York.
63. Wood SN (2006). Generalized Additive Models: An Introduction with R. Chapman & Hall/CRC.
64. Yuan M, Lin Y (2006). "Model Selection and Estimation in Regression with Grouped Variables". Journal of Royal Statistical Society B, 68, 49-67.