[1] Bondell, H., Reich, B.: Simultaneous regression shrinkage, variable selection, and supervised clustering of predictors with OSCAR. Biometrics. 64, 115-123 (2007)
[2] Bogdan, M., Van den Berg, E., Su, W.J., Candès, E.J.: Statistical estimation and testing via the sorted l1 norm. http://arxiv.org/abs/1310.1969, (2013)
[3] Zeng, X.R., Figueiredo, M.A.T.: Decreasing weighted sorted l1 regularization. IEEE Signal Process. Lett. 21, 1240-1244 (2014)
[4] Wu, B., Ding, C., Sun, D.F., Toh, K.-C.: On the Moreau-Yosida regularization of the vector k-norm related functions. SIAM J. Optim. 24, 766-794 (2014)
[5] Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imag. Sci. 2, 183-202 (2009)
[6] Wright, S., Nowak, R., Figueiredo, M.: Sparse reconstruction by separable approximation. IEEE Trans. Signal Process. 57, 2479-2493 (2009)
[7] Ivanov, V.K.: On linear problems which are not well-posed. Dokl. Akad. Nauk SSSR 145, 270-272 (1962)
[8] Morozov, V.A.: Choice of parameter for the solution of functional equations by the regularization method. Dokl. Akad. Nauk SSSR. 175, 1225-1228 (1967)
[9] Tikhonov, A.N.: Solution of incorrectly formulated problems and the regularization method. Dokl. Akad. Nauk SSSR. 151, 501-504 (1963)
[10] Zeng, X.R., Figueiredo, M.A.T.: The ordered weighted l1 norm: atomic formulation, projections, and algorithms. http://arxiv.org/abs/1409.4271 (2014)
[11] Lorenz, D., Worliczek, N.: Necessary conditions for variational regularization schemes. Inverse Probl. 29, 871 (2013)
[12] Seidman, T.I., Vogel, C.R.: Well posedness and convergence of some regularisation methods for nonlinear ill posed problems. Inverse Probl. 5, 227-238 (1989)
[13] Davis, D.: An O(n log (n)) algorithm for projecting onto the ordered weighted l1 norm ball. http://arxiv.org/abs/1505.00870 (2015)
[14] Li, Q.Z., Li, X.D.: Fast projection onto the ordered weighted ell1 norm ball. Sci. China Math. 64, doi: 10.1007/s11425-020-1743-9 (2021)
[15] Han, J.Y., Sun, D.F.: Newton and quasi-Newton methods for normal maps with polyhedral sets. J. Optim. Theory Appl. 94, 659-676 (1997)
[16] Li, X.D., Sun, D.F., Toh, K.-C.: On the efficient computation of a generalized Jacobian of the projector over the Birkhoff polytope. Math. Program. 179, 419-446 (2020)
[17] Best, M.J., Chakravarti, N.: Active set algorithms for isotonic regression. a unifying framework. Math. Program. 47, 425-439 (1990)
[18] Boyd, S., Vandenberghe, L.: Convex optimization. Cambridge University Press, New York (2004)
[19] Bonnans, J.F., Shapiro, A.: Perturbation analysis of optimization problems. Springer Verlag, New York (2000)
[20] Hiriart-Urruty, J.-B., Lemaréchal, C.: Fundamentals of convex analysis. Springer, New York (2001)
[21] Facchinei, F., Pang, J.-S.: Finite-dimensional variational inequalities and complementarity problems. Springer, New York (2003)
[22] Dai, Y.-H., Fletcher, R.: New algorithms for singly linearly constrained quadratic programs subject to lower and upper bounds. Math. Program. 106, 403-421 (2006)
[23] Rockafellar, R.T., Wets, R.J.-B.: Variational analysis. Springer, Berlin (1998)
[24] Potra, F.A., Qi, L.Q., Sun, D.F.: Secant methods for semismooth equations. Numer. Math. 80, 305-324 (1998)
[25] Ayer, M., Brunk, H.D., Ewing, G.M., Reid, W.T., Silverman, E.: An empirical distribution function for sampling with incomplete information. Ann. Math. Stat. 26, 641-647 (1955)
[26] Kruskal, J.B.: Nonmetric multidimensional scaling: a numerical method. Psychometrika. 29, 115-129 (1964)
[27] Miles, R.E.: The complete amalgamation into blocks, by weighted means, of a finite set of real numbers. Biometrika. 46, 317-327 (1959)
[28] Brunk, H.D., Ewing, G.M., Utz, W.R.: Minimizing integrals in certain classes of monotone functions. Pacific J. Math. 7, 833-847 (1957)
[29] Van Eeden, C.: Maximum likelihood estimation of ordered probabilities. Indag. Math. 59, 444-455 (1956)
[30] Bogdan, M., Van den Berg, E., Sabatti, C., Su, W.J., Candès, E.J.: SLOPE-adaptive variable selection via convex optimization. Ann. Appl. Stat. 9, 1103-1140 (2015)
[31] Liu, M.J., Liu, Y.-J.: Fast algorithm for singly linearly constrained quadratic programs with box-like constraints. Comput. Optim. Appl. 66, 309-326 (2017) |
