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2000 | 20 | 2 | 195-207
Tytuł artykułu

On weak sharp minima for a special class of nonsmooth functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present a characterization of weak sharp local minimizers of order one for a function f: ℝⁿ → ℝ defined by $f(x): = max{f_i(x)| i = 1,...,p}$, where the functions $f_i$ are strictly differentiable. It is given in terms of the gradients of $f_i$ and the Mordukhovich normal cone to a given set on which f is constant. Then we apply this result to a smooth nonlinear programming problem with constraints.
Rocznik
Tom
20
Numer
2
Strony
195-207
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-12-10
poprawiono
2000-05-07
Twórcy
  • Faculty of Mathematics, University of Łódź, ul. S. Banacha 22, 90-238 Łódź, Poland
Bibliografia
  • [1] J.F. Bonnans and A. Ioffe, Second-order sufficiency and quadratic growth for nonisolated minima, Math. Oper. Res. 20 (1995), 801-817.
  • [2] J.M. Borwein, Stability and regular points of inequality systems, J. Optim. Theory Appl. 48 (1986), 9-52.
  • [3] J.V. Burke and M.C. Ferris, Weak sharp minima in mathematical programming, SIAM J. Control Optim. 31 (1993), 1340-1359.
  • [4] F.H. Clarke, Yu.S. Ledyaev, R.J. Stern and P.R. Wolenski, Nonsmooth Analysis and Control Theory, Springer-Verlag, New York 1998.
  • [5] D. Pallaschke and S. Rolewicz, Foundations of Mathematical Optimization. Convex Analysis without Linearity, Kluwer Academic Publishers, Dordrecht 1997.
  • [6] R.T. Rockafellar and R.J-B. Wets, Variational Analysis, Springer-Verlag, Berlin 1998.
  • [7] M. Studniarski, Necessary and sufficient conditions for isolated local minima of nonsmooth functions, SIAM J. Control Optim. 24 (1986), 1044-1049.
  • [8] M. Studniarski, Second-order necessary conditions for optimality in nonsmooth nonlinear programming, J. Math. Anal. Appl. 154 (1991), 303-317.
  • [9] M. Studniarski, Characterizations of strict local minima for some nonlinear programming problems, Nonlinear Anal. 30 (1997), 5363-5367 (Proc. 2nd World Congress of Nonlinear Analysts).
  • [10] M. Studniarski, Characterizations of weak sharp minima of order one in nonlinear programming, System Modelling and Optimization (Detroit, MI, 1997), 207-215, Chapman & Hall/CRC Res. Notes Math., 396, 1999.
  • [11] M. Studniarski and M. Studniarska, New characterizations of weak sharp and strict local minimizers in nonlinear programming, Preprint 1999/15, Faculty of Mathematics, University of ód\'z.
  • [12] M. Studniarski and D.E. Ward, Weak sharp minima: characterizations and sufficient conditions, SIAM J. Control Optim. 38 (1999), 219-236.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1012
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