Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 24, 1992 - Issue 1-2
26
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Subgradient projection algorithms for constrained nonsmooth optimization II: nonlinear constraintsFootnote

Pages 75-90 | Published online: 20 Mar 2007

References

  • Berge , C. 1963 . Topological Spaces , New York : Macmillan .
  • Clarke , F. 1983 . Optimization and Nonsmooth Analysis Wiley, New York
  • Cullum , J. , Donath , W.E. and Wolfe , P. 1975 . The minimization of certain nondifferentiable sums of eigenvalues of symmetric matrices . Math. Prog. Study , 3 : 35 – 55 .
  • Lemarechal , C. , Strodiot , J.J. and Bihain , A. 1981 . On a bundle algorithm for nonsmooth optimization , Edited by: Mangasarian , O.L. , Meyer , R.R. and Robinson , S.M. 245 – 281 . New York : Academic Press . Nonlinear Programming 3
  • Yingiu , Lin. and Xianjian , Ye. 1990 . Subgradient projection algorithms for constrained nonsmooth optimization I: linear constraints, in Chinese . Numer. Anal. J. Chinese Univ , 13 : 270 – 283 .
  • Nguyen , V.H. and Strodiot , J.J.A. 1990 . linearly contrained algorithm not requiring derivative continuity . Engineering Structure , 6 : 7 – 11 .
  • Owens , R.W. 1984 . Implementation of subgradient projection algorithm II . Internat. J. Comput. Math , 16 : 57 – 69 .
  • Panier , E.R. 1987 . An active set method for solving linearly constrained nonsmooth optimization problems . Math. Prog , 37 : 269 – 292 .
  • Polak , E. 1987 . On the mathematical foundations of nondifferentiable optimization in engineering design . SIAM Review , 29 : 21 – 89 .
  • Polak , E. and Mayne , D.Q. 1985 . Algorithm models for nondifferentiable optimization . SIAM J. Control Optim , 23 : 477 – 491 .
  • Polak , E. and Wardi , Y.Y. 1982 . A nondifferentiable optimization algorithm for the design of control systems subject to singular value inequalities over a frequency range . Automatica , 18 : 267 – 283 .
  • Polak , E. , Mayne , D.Q. and Wardi , Y.Y. 1983 . On the extension of constrained optimization algorithms from differentiable to nondifferentiable problems . SIAM J. Control Optim , 21 : 179 – 204 .
  • Rosen , J.B. 1961 . The gradient projection method for nonlinear programming, Part II: Nonlinear constraints . J. SIAM , 9 : 514 – 532 .
  • Schultz , H.K. and Kuhn-Tucker , A. 1973 . Algorithm, SIAM J. Control , 11 : 438 – 445 .
  • Sreedharan , V.P. 1984 . Subgradient projection algorithm II . J. Approx. Theory , 41 : 217 – 243 .
  • Sreedharan , V.P. 1986 . Subgradient projection algorithm III . J. Approx. Theory , 47 : 228 – 239 .
  • Strodiot , J.J. , Nguyen , V.H.N. and Heukemes , N. 1983 . ∊-Optimal solution in nondifferentiable convex programming and some related questions . Math. Prog , 25 : 307 – 328 .
  • Xianjian Ye. Some subgradient projection algorithms for constrained nonsmooth optimization problems Nanjing University Chinese 1988 M. S. thesis
  • Xianjian Ye. Constraint qualifications for nonsmooth optimization to appear
  • Xianjian , Ye. 1991 . Subgradient projection algorithms for constrained optimization III: another algorithm for nonlinear constraints . Math. Biquarterly , 8 ( 1 ) : 56 – 65 . in Chinese, J. Nanjing Univ

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.