References
- Auslender , A. 1986 . Numerical methods for nondifferentiable convex optimizations . Mathematical Programming Study , 30 : 103 – 126 .
- Bertsekas , D. P. 1975 . Necessary and sufficient conditions for a penalty method to be exact . Mathematical Programming , 9 : 87 – 99 .
- Bertsekas , D. P. and Tseng , P. 1994 . Partial proximal minimization algorithms for convex programming . Slam Journal on Optimization , 4 : 551 – 572 .
- Bonnans , J. F. , Gilbert , J. C. , Lemaréchal , C. and Sagastizábal , C. A. 1995 . A family of variable metric proximal methods . Mathematical Programming , 68 : 15 – 47 .
- Chen , G. and Teboulle , M. 1994 . A proximal—based decomposition method for convex minimization problems . Mathematical Programming , 64 : 81 – 101 .
- Correa , R. and Lemaréchal , C. 1993 . Convergence of some algorithms for convex minimization . Mathematical Programming , 62 : 261 – 275 .
- Fukushima , M. and Qi , L. A global and superlinearly convergent algorithm for nonsmooth convex minimization . SIAM Journal on Optimization , to appear in
- Güler , O. 1991 . On the convergence of the proximal point algorithm for convex minimization . SLAM Journal on Control and Optimization , 29 : 403 – 419 .
- Güler , O. 1992 . New Proximal point algorithms for convex minimization . SIAM Journal on Optimization , 4 : 649 – 664 .
- Ha , C. D. 1990 . A generalization of the proximal point algorithm . SIAM Journal on Control and Optimization , 28 : 503 – 512 .
- Hiriart , J. —B. and Lemaréchal , C. 1993 . Convex Analysis and Minimization Algorithms , Vol. 2 , Berlin—Heidelberg : Springer—Verlag .
- Kiwiel , K. C. 1983 . An aggregate subgradient method for nonsmooth convex minimization . Mathematical Programming , 27 : 320 – 341 .
- Kiwiel , K. C. 1990 . Proximity control in bundle methods for convex nondifferentiable minimization . Mathematical Programming , 46 : 105 – 122 .
- Kort , B. W. and Bertsekas , D. P. 1976 . Combined primal—dual and penalty methods for convex programming . SJAM Journal on Control and Optimization , 2 : 268 – 294 .
- Lemaire , B. 1992 . About the convergence of the proximal method , Edited by: Pallaschke , D. 39 – 51 . Berlin : Springer . Advances in Optimization. Lecture Notes in Economics and Mathematics System
- Lemaréehal C. Sagastizábal C. An approach to variable metric methods, in: Proceeding of the 16th IFIP Conference on System Modelling and Optimization Springer—Verlag Berlin to appear
- Mifflin , R. 1995 . A quasi—second—order proximal bundle algorithm, Preprint, Department of Pure and Applied Mathematics , Washington State University . Revised version
- Moreau , J. J. 1965 . Proximite et dualite dans un espace hilbertien . Bulletin de la. Societe Mathematique de France , 93 : 273 – 299 .
- Pang , J. —S. and Qi , L. 1993 . Nonsmooth equations: Motivation and algorithms . SIAM Journal on Optimization , 3 : 443 – 465 .
- Qi , L. 1993 . Convergence analysis of some algorithms for solving nonsmooth equations . Mathematics of Operations Research , 18 : 227 – 244 .
- Qi , L. 1994 . Superlinear convergent approximate Newton methods for LC1 optimization problems . Mathematical Programming , 64 : 277 – 294 .
- Qi , L. 1994 . Second—order analysis of the Moreau—Yosida approximation of a convex function , University of New South Wales . AMR 94/20, Applied Mathematics Report
- Rockafellar , R. T. 1976 . Monotone operators and proximal point algorithm . SIAM Journal on Control and Optimization , 14 : 877 – 898 .
- Rockafellar , R. T. 1976 . Augmented Lagrangians and applications of the proximal point algorithm in convex programming . Mathematics of Operations Research , 1 : 97 – 116 .
- Wu , S. Q. 1992 . Convergence properties of descent methods for unconstrained minimization . Optimization , 26 : 229 – 237 .