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Local cone approximations in optimization

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We show how to use intensively local cone approximations to obtain results in some fields of optimization theory such as optimality conditions, constraint qualifications, mean value theorems and error bound.
Rocznik
Strony
583--600
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
  • Department of "Sistemi ed Istituzioni per L'Economia", University of L'Aquila
Bibliografia
  • AUSSEL, D., CORVELLEC, J.-N. and LASSONDE, M. (1995) Mean value property and subdifferential criteria for lower semicontinuous functions. Trans. Amer. Math. Soc. 347, 4144-4161.
  • AZE, D. (2003) A survey on error bounds for lower semicontinuous functions. In: Proceedings of 2003 MODE-SMAI Conference 13, 1-17.
  • BEN-ISRAEL, A. and MOND, B. (1986) What is invexity? J. Austral. Math. Soc. Ser. B 28, 1-9.
  • CASTELLANI, M. (2000) A dual representations for proper positively homogeneous functions. J. Global Optim. 16, 393-400.
  • CASTELLANI, M. (2001) Nonsmooth invex functions and sufficient optimality conditions. J. Math. Anal. Appl. 255, 319-332.
  • CASTELLANI, M. (2006) On constraint qualifications in nonlinear programming. Submitted.
  • CASTELLANI, M., D’OTTAVIO, A. and GIULI, M. (2003) A mean value theorem for K-directional epiderivatives. In: G.P. Crespi et al., eds., Recent Advances in Optimization, 21-34.
  • CASTELLANI, M. and PAPPALARDO, M. (1995) First order cone approximations and necessary optimality conditions. Optimization 35, 113-126.
  • CRAVEN, B.D. (1981) Invex functions and constrained local minima. Bull. Austral. Math. Soc. 24, 357-366.
  • CRAVEN, B.D. and GLOVER, B.M. (1985) Invex functions and duality. J. Austral. Math. Soc. Ser. A 39, 1-20.
  • DEMYANOV, V.F. and RUBINOV, A.M. (1995) Constructive Nonsmooth Analysis. Peter Lang, Frankfurt am Main.
  • ELSTER, K.H. and THIERFELDER, J. (1988) Abstract cone approximations and generalized differentiability in nonsmooth optimization. Optimization 19, 315-341.
  • GLOVER, B.M., ISHIZUKA, Y., JEYAKUMAR, V. and TUAN, H.D. (1996) Complete characterizations of global optimality for problems involving the pointwise minimum of sublinear functions. SIAM J. Optim. 6, 362-372.
  • HANSON, M.A. (1981) On sufficiency of the Kuhn-Tucker conditions. J. Math. Anal Appl. 80, 545-550.
  • HOFFMAN, A.J. (1952) On approximate solutions of systems of linear inequalities. J. Res. Nat. Bur. Standards 49, 263-265.
  • JEYAKUMAR, V. (1987) On optimality conditions in nonsmooth inequality constrained minimization. Numer. Fund. Anal. Optim. 9, 535-546.
  • KAUL, R.N. and KAUR, S. (1985) Optimality criteria in nonlinear programming involving nonconvex functions. J. Math. Anal. Appl. 105,104-112.
  • KOMLOSI, S. and PAPPALARDO, M. (1994) A general scheme for first order approximations in optimization. Optim. Methods Softw. 3, 143-152.
  • REILAND, T.W. (1990) Nonsmooth invexity. Bull. Austral. Math. Soc. 42, 437-446.
  • THIBAULT, L. (1995) A note on the Zagrodny mean value theorem. Optimization 35,127-130.
  • THIBAULT, L. and ZAGRODNY, D. (1985) Integration of subdifferentials of lower semicontinuous functions on Banach spaces. J. Math. Anal. Appl. 189,33-58.
  • VLACH, M. (1970) On necessary conditions of optimality in linear space. Comment. Math. Univ. Carolin. 11, 501-513.
  • WARD, D.E. (1991) Chain rules for nonsmooth functions. J. Math. Anal. Appl. 158, 519-538.
  • WARD, D.E. and BORWEIN, J.M. (1987) Nonsmooth calculus in finite dimensions. SIAM J. Control Optim. 25, 1312-1340.
  • WU, Z. and YE, J.J. (2001) Sufficient conditions for error bounds. SIAM J. Optim. 12, 421-435.
  • WU, Z. and YE, J.J. (2002) On error bounds for lower semicontinuous functions. Math. Programming 92, 301-314.
  • YE, Y.L. (1991) d-invexity and optimality conditions. J. Math. Anal. Appl. 162, 242-249.
  • ZAGRODNY, D. (1988) Approximate mean value theorem for upper subderiv-atives. Nonlinear Anal. 12, 1413-1428.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0017-0056
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