References
- Achtziger , W. 1997 . “ Topology optimization of discrete structures: An introduction in view of computational and nosmooth aspects ” . In Topology Optimization in Structural Mechanics , Vol. 374 , 57 – 100 . Vienna : Springer . CISM Courses and Lectures
- Alizadeh , F. and Goldfarb , D. 2003 . Second-order cone programming . Math. Program. Ser. B , 95 ( 1 ) : 3 – 51 .
- Alvarez , F. and Carrasco , M. 2005 . Minimization of the expected compliance as an alternative approach to multiload truss optimization . Struct. Multidiscip. Optim. , 29 ( 6 ) : 470 – 476 .
- Auslender , A. 2003 . Variational inequalities over the cone of semidefinite positive matrices and over the Lorentz cone . Optim. Methods Softw. , 18 ( 4 ) : 359 – 376 .
- Auslender , A. and Teboulle , M. 2003 . Asymptotic Cones and Functions in Optimization and Variational Inequalities , New York : Springer-Verlag . Springer Monographs in Mathematics
- Auslender , A. and Teboulle , M. 2006 . Interior gradient and proximal methods for convex and conic optimization . SIAM J. Optim. , 16 ( 3 ) : 697 – 725 .
- Ben-Tal , A. and Nemirovski , A. 2001 . Lectures on Modern Convex Optimization , Philadelphia : Society for Industrial Mathematics . MPS-SIAM Series on Optimization
- Bonnans , J. F. , Gilbert , J. Ch. , Lemachéral , C. and Sagastizábal , C. A. 1995 . A family of variable metric proximal methods . Math. Program. Ser. A , 68 ( 1 ) : 15 – 47 .
- Burke , J. V. and Qian , M. 1999 . A variable metric proximal point algorithm for monotone operators . SIAM J. Control Optim. , 37 ( 2 ) : 353 – 375 .
- Burke , J. V. and Qian , M. 2000 . On the superlinear convergence of the variable metric proximal point algorithm using Broyden and BFGS matrix secant updating . Math. Program. Ser. A , 88 ( 1 ) : 157 – 181 .
- Censor , Y. and Zenios , S. A. 1992 . The proximal minimization algorithm with D-function . J. Optim. Theory Appl. , 73 ( 3 ) : 451 – 464 .
- Chen , G. and Teboulle , M. 1993 . Convergence analysis of proximal-like minimization algorithm using Bregman functions . SIAM J. Optim. , 3 ( 3 ) : 538 – 543 .
- Cortes , C. and Vapnik , V. 1995 . Support-vector networks . Mach. Learn. , 20 : 273 – 297 .
- Eckstein , J. 1993 . Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming . Math. Oper. Res. , 18 ( 1 ) : 202 – 216 .
- Faraut , J. and Koranyi , A. 1994 . Analysis on Symmetric Cones , New York : Oxford University Press . Oxford Mathematical Monographs
- Fukushima , M. , Luo , Z.-Q. and Teng , P. 2001/2002 . Smoothing functions for second-order cone complementary problems . SIAM J. Optim. , 12 ( 2 ) : 436 – 460 .
- J.Ch. Gilbert, Optimisation Différentiable – Théorie et Algorithmes. Syllabus de cours à I'ENSTA, 2002. Avaliable at http://www-rocq.inria.fr/~gilbert/ensta/optim.html
- Güler , O. 1991 . On the convergence of the proximal point algorithm for convex minimization . SIAM J. Control Optim. , 29 ( 2 ) : 403 – 419 .
- Hiriart-Urruty , J.-B. and Lemaréchal , C. 1993 . Convex Analysis and Minimization Algorithms II: Advanced Theory and Bundle Methods. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] , Vol. 306 , Berlin : Springer-Verlag .
- Horn , R. and Johnson , C. 1990 . Matrix Analysis , Cambridge University Press .
- Iusem , A. N. 1995 . An interior multiplicative method for optimization under positivity constraints . Acta Appl. Math. , 38 : 163 – 184 .
- Knopp , K. 1951 . Theory and Application of Infinite Series , Glasgow : Blackie & Son .
- Lemarèchal , C. and Sagastizábal , C. 1997 . Variable metric bundle methods: From conceptual to implementable forms . Math. Program. , 76 : 393 – 410 .
- Lewis , A. S. 1996 . Convex Analysis on the Hermitian Matrices . SIAM J. Optim. , 6 ( 1 ) : 164 – 177 .
- Lobo , M. S. , Vandenberghe , L. , Boyd , S. and Lebret , H. 1998 . Applications of second-order cone programming . Linear Algebra Appl. , 284 ( 1–3 ) : 193 – 228 .
- Martinet , B. 1978 . Perturbation des methodes d'optimisation, aplication . RAIRO anal. Numer. , 12 : 153 – 171 .
- Moreau , J. J. 1965 . Proximité et dualité dans um espace Hilbertien . Bull. Soc. Math. France , 93 : 273 – 299 .
- Oliveira , G. L. , Souza , S. S. , da Cruz Neto , J. X. and Oliveira , P. R. 2009 . Interior proximal methods for optimization over the positive orthant . preprint
- Peng , J. , Roos , C. and Terlaky , T. 2002 . Primal-dual interior-point methods for second-order conic optimization based on self-regular proximities . SIAM J. Optim. , 13 ( 1 ) : 179 – 203 .
- Polyak , R. A. 1987 . Introduction to Optimization , New York : Optimization Software .
- Qian , M. 1992 . The Variable Metric Proximal Point Algorithm: Theory and Application , Seattle, WA : University of Washington . Ph.D. thesis
- Rockafellar , R. T. 1970 . Convex Analysis , Princeton, NJ : Princeton University Press .
- Rockafellar , R. T. 1976 . Monotone operators and the proximal point algorithm . SIAM J. Control Optim. , 14 ( 5 ) : 877 – 898 .
- Saketha Nath , J. and Bhattacharyya , C. Maximum margin classifiers with specified false positive and false negative error rates . Proceedings of the Seventh SIAM International Conference on Data Mining . pp. 26 – 28 . April 2007, Minneapolis, Minnesota http://www.siam.org/meetings/proceedings/2007/datamining/papers/004Jagarlapudi.pdf
- Shivaswamy , P. K. , Bhattacharyya , C. and Smola , A. J. 2006 . Second order cone programming approaches for handling missing and uncertain data . J. Mach. Learn. Res. , 7 : 1283 – 1314 .
- Sturm , J. F. 1999 . Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones . Optim. Methods Softw. , 11 ( 1–4 ) : 625 – 653 . Available at http://sedumi.ie.lehigh.edu/
- Tsuchiya , T. 1999 . A convergence analysis of the scaling-invariant primal-dual path-following algorithms for second- order cone programming . Optim. Methods Softw. , 11 ( 1–4 ) : 141 – 182 .