Stability properties of weak sharp minima

• Autorzy: Studniarski M. , Taha A. W. A.
• Języki publikacji: EN

Abstrakty

EN

In this paper, stability theorems of Studniarski (1989) are extended to include the stability of weak sharp local minimum points for a nonsmooth mathematical programming problem.

Słowa kluczowe

EN

nonlinear programming; weak sharp minima; stability; Lipschitzian functions

PL

programowanie nieliniowe; stabilność; funkcja Lipschitza

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2003
• Tom: Vol. 32, no 2
• Strony: 351--359
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Studniarski M.

• Faculty of Mathematics, University of Łódź, ul. S. Banacha 22, 90-238 Łódź, Poland

autor

Taha A. W. A.

• College of Engineering, Al-Mustansirya University, Baghdad, Iraq

Bibliografia

• BONNANS, J.F., IOFFE, A. (1995) Second-order sufficiency and quadratic growth for nonisolated minima. Math. OpeT. Res., 20, 801-817.
• BURKE, J .V. and FERRIS, M.C. (1993) Weak sharp minima in mathematical programming. SIAM J. Contr·ol Optim., 31, 1340- 1359.
• CLARKE, F.H. (1983) Optimization and Nonsmooth Analysis. New York, Wileylnterscience.
• HYERS, D.H. (1978) On the stability of minimum points. J. Math. Anal. Appl., 62, 530-537.
• HYERS, D.H. (1985) Stability of minimum points for problems with constraints. In: DijJeTential GeornetTy, Calc'Ul'Us of VaTiations, and the·iT Applications, Dedic. Mern. L. BuleT 200th Anniv. Death, Lect. Notes Pure Appl. Math., 100, 283-289.
• KLATTE, D. (1994) On quantitative stability for non-isolated minima. ContTol CybeTnet., 23, 183- 200.
• STUDNIARSKI, M. (1989) Sufficient conditions for stability of local minimum points in nonsmooth optimization. Optirnization, 20, 27-35.
• STUDNIARSKI, M. (1999) Characterizations of weak sharp minima of order one in nonlinear programming. In: System Modell-ing and Optirnization (Detroit, MI, 1997}, Chapman & Hall/CRC Res. Notes Math., 396, 207-215.
• STUDNIARSKI, M. and WARD, D.E. (1999) Weak sharp minima: characterizations and sufficient conditions. SIAM J. Contwl Optim. 38, 219-236.
• WARD, D. (1998) Sufficient conditions for weak sharp minima of order two and directional derivatives of the value function. In: A. V. Fiacco, ed. Mathematical Programrning with Data PeTt·uTbations. Lect. Notes Pure Appl. Math., 195, Dekker, New York, 419-436.