Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 57, 2008 - Issue 4
101
Views
30
CrossRef citations to date
0
Altmetric
Original Articles

Higher-order necessary and sufficient conditions for strict local pareto minima in terms of Studniarski's derivatives

Pages 593-605 | Received 16 Dec 2004, Accepted 31 Oct 2006, Published online: 23 May 2008

References

  • Aubin , JP and Frankowska , H . 1990 . Set-Valued Analysis , Boston : Birkhaüser .
  • Auslender , A . 1984 . Stability in mathematical programming with nondifferentiable data. . SIAM Journal of Control and Optimization , 22 : 239 – 254 .
  • Borwein , JM . 1980 . The geometry of Pareto efficiency over cones. . Mathematical Operations forsch und Statistical Series Optimization , 11 : 235 – 248 .
  • Cromme , L . 1978 . Strong Uniqueness: a far reaching criterion for the convergence of iterative procedures. . Numer Mathemati , 29 : 179 – 193 .
  • Giorgi , G and Guerraggio , A . 1992 . On the notion of tangent cone in mathematical programming. . Optimization , 25 : 11 – 23 .
  • Hestenes , MR . 1981 . Optimization Theory: The Finite-Dimensional Case , New York : Robert E. Krieger Publishing Company .
  • Ioffe , AD . 1984 . Calculus of Dini subdifferentials of functions and contingent coderivatives of set-valued maps. . Nonlinear Analysis , 8 : 517 – 539 .
  • Jiménez , B . 2002 . Strict efficiency in vector optimization. . Journal of Mathematical Analysis and Applications , 265 : 264 – 284 .
  • Jiménez , B . 2003 . Strict minimality conditions in nondifferentiable multiobjective programming. . Journal of Optimization Theory and Applications , 116 : 99 – 116 .
  • Jiménez , B and Novo , V . 2003 . First and second order sufficient conditions for strict minimality in nonsmooth vector optimization. . Journal of Mathematical Analysis and Applications , 284 : 496 – 510 .
  • Kien , PT and Luu , DV . 2003 . Higher-order optimality conditions for isolated local minima. . Nonlinear Functional Analysis and Applications , 8 : 35 – 48 .
  • Maurer , H and Zowe , J . 1979 . First and second-order necessary and suffiient optimality conditions for infinite dimensional programming problems. . Mathamatical Programming , 16 : 98 – 110 .
  • Studniarski , M . 1986 . Necessary and sufficient conditions for isolated local minima of nonsmooth functions. . SIAM Journal of Control and Optimization , 24 : 1044 – 1049 .
  • Ward , DE . 1994 . Characterizations of strict local minima and necessary conditions for weak sharp minima. . Journal of Optimization Theory and Applications , 80 : 551 – 571 .

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.