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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 37, 1996 - Issue 2
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Original Articles

Second-order necessary optimality conditions via directional regularity

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Pages 113-124 | Published online: 20 Mar 2007

References

  • Aubin , J. and Ekeland , I. 1984 . Applied Nonlinear Analysis , New York : Wiley .
  • Ben-Tal , A. and Zowe , J. 1992 . A unified theory of first and second order conditio ns for extrem um problems in topolo gical vecto r spaces . Math. Prog. Study , 19 : 39 – 76 .
  • Ben-Tal , A. and Zowe , J. 1982 . Necessary and sufficient optimality conditions for a class of non smooth minimization problem . Math . Prog , 24 : 70 – 91 .
  • Borwein , J.M. 1986 . Stability and regular points of inequality systems . J. Optimiz. Theory Appl , 48 : 9 – 51 .
  • Chaney , R.W. 1986 . Second-order necessary conditions in semismooth optimization . Math. Proq , 40 : 95 – 109 .
  • Clarke , F.H. 1983 . Optimization and Nonsmooth Analysis , New York : Wiley .
  • Dien , P.H. and Sach , P.H. 1989 . Second-order optimality cond itions for the extremum problem under inclusion constraints . Applied Math . Optimiz , 20 : 71 – 80 .
  • Dien , P.H. 1985 . On the regularity for the extremal problem under locally Lipschitz inclusion constraints . Applied Math. Optimiz , 13 : 151 – 161 .
  • Furukawa , N. and Yoshinaga , Y. 1988 . Higher-order variational sets, variational derivatives and higher-order necessary conditions in abstract mathematical programming . Bulletin of lnformatics and Cybernetics , 23 : 9 – 40 .
  • Hiriart-Urruty , J.B. , Strodiot , J.J. and Hien Nguyen , V. 1984 . Generalized Hessian matrix and second-order conditions for a problem with C 1.1 data . Appl. Math. Optimiz , 11 : 43 – 56 .
  • Hoffmann , K.H. and Kornstaedt , H.J. 1978 . Higher-order necessary conditions in abstract mathematical programming . J. Optimiz, Theory Appl , 26 : 533 – 568 .
  • Ioffe , A. 1979 . Regular points of Lipschitz functions . Trans. Amer. Math. Soc , 251 : 61 – 69 .
  • Linnemann , A. 1982 . Higher-order necessary conditions for infinite and semi-infinite optimization . J. Optimiz, Theory Appl , 38 : 483 – 511 .
  • Penot , J.P. 1985 . Generalized higher order derivatives and higher order optimality conditions, preprint , University de Pau .
  • Sach , P.H. 1990 . Second-order necessary optimality conditions for optimization problems involving set-valued maps . Applied Math. Optimiz , 22 : 189 – 209 .
  • Studniarski , M. 1991 . Second-order necessary conditions for optimality in nonsmooth nonlinear programming . J. Math. Anal. Appl , 154 : 303 – 317 .
  • Yang , X.Q. and Jeyakumar , V. 1992 . Generalized second-order directional derivatives and optimizalton with C 1.1 functions . Optimization , 26 : 165 – 185 .

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