252
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Second-order analysis of the Moreau–Yosida and the Lasry–Lions regularizations

Pages 109-116 | Received 29 Nov 2008, Published online: 16 Oct 2009

References

  • Attouch , H. and Aze , D. 1993 . Approximation and regularization of arbitrary functions in Hilbert space by the Lasry-Lions method . Ann. Inst. Henri Poincare , 10 ( 3 ) : 289 – 312 .
  • Borwein , J. M. and Lewis , A. S. 2006 . Convex Analysis and Nonlinear Optimization. Theory and Examples , New York : Springer .
  • Borwein , J. M. and Zhu , Q. J. 2005 . Techniques of Variational Analysis , New York : Springer .
  • Burke , J. and Qian , M. 1999 . A variable metric proximal point algorithm for monotone operators . SIAM J. Control Optim. , 37 ( 2 ) : 353 – 375 .
  • Chen , X. and Fukushima , M. 1999 . Proximal quasi-Newton methods for nondifferentiable convex optimization . Math. Program. , 85 ( 2A ) : 313 – 334 .
  • Clarke , F. 1983 . Optimisation and Nonsmooth Analysis , New York : Society for Industrial Mathematics .
  • Fukushima , M. and Qi , L. 1996 . A globally and superlinearly convergent algorithm for nonsmooth convex minimization . SIAM J. Optim. , 6 ( 4 ) : 1106 – 1120 .
  • Georgiev , P. G. and Zlateva , N. P. 2000 . Reconstructions of subdifferentials by the Lasry-Lions regularizations . J. Math. Anal. Appl. , 248 : 415 – 428 .
  • Lasry , J. M. and Lions , P. L. 1986 . A remark on regularization in Hilbert spaces . Israel J. Math. , 55 : 257 – 266 .
  • Lemaréchal , C. and Sagastizábal , C. 1997 . Practical aspects of the Moreau–Yosida regularization: theoretical preliminaries . SIAM J. Optim. , 7 ( 2 ) : 367 – 385 .
  • Lemaréchal , C. and Sagastizábal , C. 1997 . Variable metric bundle methods: from conceptual to implementable forms . Math. Program. , 76 ( 3B ) : 393 – 410 .
  • Loewen , P. D. 1993 . Optimal control via nonsmooth analysis , Vol. 2 , Providence, RI : American Mathematical Society . CRM-AMS Lecture Notes in Mathematics
  • Mifflin , R. 1996 . A quasi-second-order proximal bundle algorithm . Math. Program. , 73 : 51 – 72 .
  • 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
  • Qian , M. 1992 . “ The variable metric proximal point algorithm: theory and application ” . University of Washington . Ph.D. Thesis
  • Poliquin , R. A. and Rockafellar , R. T. 1996 . Generalized Hessian properties of regularized nonsmooth functions . SIAM J. Optim. , 6 : 1121 – 1137 .
  • Poliquin , R. A. and Rockafellar , R. T. 1995 . “ Second-order Nonsmooth Analysis in Nonlinear Programming ” . In Recent Advances in Optimization , 322 – 350 . Singapore : World Scientific .
  • Poliquin , R. A. and Rockafellar , R. T. 1996 . Prox-regular functions in variational analysis . Trans. Amer. Math. Soc. , 348 : 1805 – 1838 .
  • Rockafellar , R. T. and Wets , R.-B. 1998 . Variational Analysis , Berlin : Springer .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.