Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 20, 1989 - Issue 2
23
Views
11
CrossRef citations to date
0
Altmetric
Original Articles

A survey of conical approximations used in the optimization

Pages 147-161 | Received 01 Mar 1987, Published online: 27 Jun 2007

References

  • Abadie , J. 1967 . Nonlinear Programming , North Holland Publishing Company .
  • Bazaraa , M.S. , Goode , J.J. and Nashed , M.Z. 1974 . On the Cone of Tangents with Applications to Mathematical Programming . J. Optim. Theory Appl , 13
  • Boltjanskij , V.G. 1975 . Metod šatrov v teorii ekstremalnych zadač . Uspechi matema-ticeskich nauk , XXX ( 3 ) : 183
  • Borwein , J.M. 1982 . Necessary and Sufficient Conditions for Quadratic Minimality.Numer . Funct. Anal. Optim , 5 ( 3 ) : 2
  • Borwein , J.M. and Strojwas , H.M. 1986 . Proximal Analysis and Boundaries of Closed Setsin Banach Space. Part I . Theory. Can. J. Math , XXXVIII ( 2 )
  • Canon , M.D. , Cullum , C.D. Jr and Polak , E. 1970 . Theory of Optimal Control and Mathematical Programming , McGraw-Hill .
  • Clarke , F.H. 1975 . Generalized Gradients and Applications . Trans. Amer. Math. Soc , 205
  • Cornet , B. 1987 . Regularity Properties of Open Tangent Cones . Math. Prog. Study , 30
  • Demjanov , V.F. and Rubinov , A.M. 1968 . Približennyje metody rešenija ekstremalnychzadač . Izdatelstvo leningradskovo universiteta , 30
  • Dolecki , S. 1982 . Tangency and Differentiation: Some Applications of Convergence Theory . Ann. Mat. Pura Appl , IV ( CXXX )
  • Dolecki , S. 1983 . Hypertangent Cones for a Special Class of Sets. Optimization: Theory and Algorithms , Edited by: Hiriart-Urruty , Oettli and Stoer . New York : M. Dekker .
  • Dubovitskij , A.Ja and Miljutin , A.A. 1965 . Zadačl na ekstremum pri naličii ograničenij . Ž. vyčisl. mat. mat. fiz , 5
  • Elster , K.H. and Thierfelder , J. 1985 . The General Concept of Cone Approximations in Nondifferentiable Optimization . Lecture Notes in Eeon. and M. Systems , 5
  • Guignard , M. 1969 . Generalized Kuhn-Tucker Conditions for Mathematical Programming Problems in a Banach Space . SIAM J. Control , 7 : 2
  • Hestenes , M.R. 1966 . Calculus of variations and Optimal Control Theory , John Wiley .
  • Hiriart-Urruty , J.B. 1979 . Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces . Math. Oper. Research , 4
  • Hiriart-Urruty , J. 1979 . “ New Concepts in Nondifferentiable Programming ” . In Bull Soc. Math , Vol. 60 , de France . Mémoire
  • Lasiecka , I. 1975 . Conical Approximations of Sets in Optimization Theory . Control and Cybernetics , 4
  • Neustadt , L.W. 1966 . An Abstract Variational Theory with Applications to a Broad Class of Optimization Problems . I. General Theory. J. SIAM Control , 4
  • Nožička , F. 1976 . Über einfache Mannigfaltigkeiten im linearen affinen Raum An in globaler Auffassung . Czech. Math. J , 6
  • Palata , J. 1980 . Eine hinreichende Bedingung fur die Existenz eines eindeutigen lokalen Extremums . Math, Operationsforsch. Statist., Ser. Optimization , 11 : 4
  • Penot , J.P. 1981 . A Characterization of Tangential Regularity . Nonlin. Anal. Th. Meth Appl , 5
  • Penot , J.P. 1985 . Characterization of Clarke's Strict Tangent Cone via Nonlinear Semigroups . Proc. Amer. Math. Soc , 93 : 1
  • Pšeničnyj , B.N. 1969 . Neobchodirnyje uslovija ekstremuma Moskva
  • Rockafellar , R.T. 1980 . Generalized Directional Derivatives and Subgradients of Nonconvex Functions . Can. J. Math , XXXII ( 2 )
  • Rockafellar , R.T. 1981 . “ Theory of Subgradients and its Application to Problems of Optimization ” . In Convex and Nonconvex Functions , Berlin : Helderman Verlag .
  • Sachs , E. 1978 . Differentiability in Optimization Theory . Math. Operationsforsch. Statist., Ser. Optim , 9 : 4
  • Thibault , L. 1983 . Tangent Cones and Quasi-Interiorly Tangent Cones to Multifunctions . Trans. Amer. Math. Soc , 277 : 2
  • Ursescu , C. 1982 . Tangent Sets' Calculus and Necessary Conditions for Extremality . SIAM J. Control and Optim , 20 : 4
  • Vlach , M. 1981 . Approximation Operators in Optimization Theory . Z. Oper. Res , 25
  • Wibrzeicki , A.P. 1972 . Maximum Principle for Semiconvex Performance Functionals . SIAM J. Control , 10 : 3
  • Zlobec , S. 1970 . Asymptotic Kuhn-Tucker Conditions for Mathematical Programming Problems in a Banach Space . SIAM J. Control , 8 : 4

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.