ReferencesA. A. Gudkov, S. V. Mironov, S. P. Sidorov, S. V. Tyshkevich“A dual active set algorithm for optimal sparse convex regression”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2019, Volume 23, Number 1,Pages 113

A dual active set algorithm for optimal sparse convex regression
A. A. Gudkov, S. V. Mironov, S. P. Sidorov, S. V. Tyshkevich



REFERENCES

1.	Burdakov O., Sysoev O., “A Dual Active-Set Algorithm for Regularized Monotonic Regression”, J. Optim. Theory Appl., 172:3 (2017), 929–949
2.	Brezger A., Steiner W. J., “Monotonic Regression Based on Bayesian P-Splines: An application to estimating price response functions from store-level scanner data”, J. Bus. Econ. Stat., 26:1 (2008), 90–104
3.	Chen Y., Aspects of Shape-constrained Estimation in Statistics, PhD Thesis, University of Cambridge, Cambridge, UK, 2013 https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.648300
4.	Balabdaoui F., Rufibach K., Santambrogio F., “Least-squares estimation of two-ordered monotone regression curves”, J. Nonparametric Stat., 22:8 (2010), 1019–1037
5.	Hazelton M. L., Turlach B. A., “Semiparametric Regression with Shape-Constrained Penalized Splines”, Comput. Stat. Data Anal., 55:10 (2011), 2871–2879
6.	Lu M., “Spline estimation of generalised monotonic regression”, J. Nonparametric Stat., 27:1 (2014), 19–39
7.	Robertson T., Wright F. T. Dykstra R. L., Order Restricted Statistical Inference, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, Chichester (UK) etc., 1988, xix+521 pp.
8.	Barlow R. E. Brunk H. D., “The Isotonic Regression Problem and its Dual”, J. Amer. Stat. Assoc., 67:337 (1972), 140–147
9.	Dykstra R. L., “An Isotonic Regression Algorithm”, J. Stat. Plan. Inf., 5:1 (1981), 355–363
10.	Best M. J., Chakravarti N., “Active set algorithms for isotonic regression: A unifying framework”, Mathematical Programming, 47:3 (1990), 425–439
11.	Best M. J., Chakravarti N., Ubhaya V. A., “Minimizing Separable Convex Functions Subject to Simple Chain Constraints”, SIAM J. Optim., 10:3 (2000), 658–672
12.	Ahuja R. K., Orlin J. B., “A Fast Scaling Algorithm for Minimizing Separable Convex Functions Subject to Chain Constraints”, Operations Research, 49:1 (2001), 784–789
13.	Strömberg U., “An Algorithm for Isotonic Regression with Arbitrary Convex Distance Function”, Comput. Stat. Data Anal., 11:2 (1991), 205–219
14.	Hansohm J., “Algorithms and Error Estimations for Monotone Regression on Partially Preordered Sets”, J. Multivariate Analysis, 98:5 (2007), 1043–1050
15.	Burdakow O., Grimvall A., Hussian M., “A Generalised PAV Algorithm for Monotonic Regression in Several Variables”, COMPSTAT, Proceedings in Computational Statistics, 16th Symposium Held in Prague, Czech Republic, v. 10, ed. J. Antoch, Springer-Verlag, New York, 2004, 761–767 http://users.mai.liu.se/olebu87/PAPERS/COMPSTAT04.pdf
16.	Dykstra R. L., Robertson T., “An Algorithm for Isotonic Regression for Two or More Independent Variables”, Ann. Statist., 10:3 (1982), 708–716
17.	Sidorov S. P., Faizliev A. R., Gudkov A. A., Mironov S. V., “Algorithms for Sparse $k$-Monotone Regression”, Integration of Constraint Programming, Artificial Intelligence, and Operations Research, Lecture Notes in Computer Science, 10848, ed. W.-J. van Hoeve, Springer International Publishing, Cham, 2018, 546–556
18.	Bach F. R., Efficient Algorithms for Non-convex Isotonic Regression through Submodular Optimization, 2017, arXiv: 1707.09157 [cs.LG]
19.	Altmann D., Grycko Eu., Hochstättler W., Klützke G., Monotone smoothing of noisy data, Technical Report feu-dmo034.15, FernUniversität in Hagen, 2014 https://www.fernuni-hagen.de/mathematik/DMO/pubs/feu-dmo034-14.pdf
20.	Gorinevsky D. M., Kim S.-J., Beard Sh., Boyd S. P., Gordon G., “Optimal Estimation of Deterioration From Diagnostic Image Sequence”, {IEEE} Transactions on Signal Processing, 57:3 (2009), 1030–1043
21.	Hastie T. Tibshirani R. Wainwright M., Statistical Learning with Sparsity: The Lasso and Generalizations, Monographs on Statistics and Applied Probability, 143, Chapman and Hall/CRC, New York, 2015, xvi+351 pp.
22.	Cai Y., Judd K. L., “Advances in Numerical Dynamic Programming and New Applications”, Handbook of Computational Economics, v. 3, eds. K. Schmedders, K. L. Judd, Elsevier, 2014, 479–516
23.	Boytsov D. I., Sidorov S. P., “Linear approximation method preserving $k$-monotonicity”, Sib. Èlektron. Mat. Izv., 12 (2015), 21–27
24.	Cullinan M. P., “Piecewise Convex-Concave Approximation in the Minimax Norm”, Abstracts of Conference on Approximation and Optimization: Algorithms, Complexity, and Applications (June 29–30, 2017, Athens, Greece), eds. I. Demetriou, P. Pardalos, National and Kapodistrian University of Athens, Athens, 2017, 4
25.	Shevaldin V. T., Approksimatciia lokalnymi splainami [Local approximation by splines], Ural Branch of RAS, Ekaterinburg, 2014, 198 pp. (In Russian)
26.	Leeuw J. Hornik K. Mair P., “Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods”, J. Stat. Softw., 32:5 (2009), 1–24
27.	Li G., Pong T. K., “Calculus of the Exponent of Kurdyka–Łojasiewicz Inequality and Its Applications to Linear Convergence of First-Order Methods”, Found. Comput. Math., 18:5 (2017), 1199–1232, arXiv: 1602.02915 [math.OC]

REFERENCES