Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We extend some necessary and sufficient conditions for strict local Pareto minima of order m obtained by Jiménez (2002) to the case of weak ψ-sharp local Pareto minima, i.e., to the case when the local solution is not necessarily unique.
Czasopismo
Rocznik
Tom
Strony
925--937
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- Faculty of Mathematics and Computer Science, University of Lodz, ul. S. Banacha 22, 90-238 Lodz, Poland, marstud@math.uni.lodz.pl
Bibliografia
- BEDNARCZUK, E. (2004) Weak sharp efficiency and growth condition for vector-valued functions with applications. Optimization 53, 455 474.
- BEDNARCZUK, E. (2006) Stability analysis for parametric vector optimization problems. Dissertationes Math. 442, 1-126.
- BONNANS, J.F. and IOFFE, A. (1995) Second-order sufficiency and quadratic growth for nonisolated minima. Math. Oper. Res. 20, 801 817.
- BURKE, J.V. and DENG, S. (2002) Weak sharp minima revisited. Part I: basic theory. Control Cybernet. 31, 439 469.
- BURKE, J.V. and DENG, S. (2005) Weak sharp minima revisited, Part II: application to linear regularity and error bounds. Math. Program. 104, 235-261.
- BURKE, J.V. and FERRIS, M.C. (1993) Weak sharp minima in mathematical programming. SIAM J. Control Optim. 31, 1340 1359.
- CLARKE, F.H. (1983) Optimization and Nonsmooth Analysis. New York, Wiley-Interscience.
- CORNEJO, O., JOURANI, A. and ZALINESCU, C. (1997) Conditioning and upper-Lipschitz inverse subdifferentials in nonsmooth optimization problems. J. Optim. Theory Appl. 95, 127-148.
- GÖPFERT, A., RIAHI, H., TAMMER, CH. and ZALINESCU,C. (2003) Variational Methods in Partially Ordered Spaces. Springer, New York.
- JIMENEZ, B. (2002) Strict efficiency in vector optimization. J. Math. Anal. Appl. 265, 264 284.
- KHAN, M.A. (1999) The Mordukhovich normal cone and the foundations of welfare economics. J. Public Economic Theory 1, 309-338.
- KLATTE, D. (1994) On quantitative stability for non-isolated minima. Control Cybernet. 23, 183-200.
- MORDUKHOVICH, B.S. (2006) Variational Analysis and Generalized Differentiation, Vol. I: Basic Theory, Vol. II: Applications. Springer, Berlin.
- NG, K.F. and ZHENG, X.Y. (2003) Global weak sharp minima on Banach spaces. SIAM J. Control Optim. 41, 1868-1885.
- PALLASCHKE, D. and ROLEWICZ, S. (1997) Foundations of Mathematical Optimization. Convex Analysis without Linearity. Kluwer Academic Publishers, Dordrecht.
- STUDNIARSKI, M. (1999) Characterizations of weak sharp minima of order one in nonlinear programming. In: System Modelling and Optimization (Detroit, MI, 1997), Chapman & Hall/CRC Res. Notes Math., 396, 207-215.
- STUDNIARSKI, M. (2000) On weak sharp minima for a special class of non-smooth functions. German-Polish Conference on Optimization - Methods and Applications (Żagań, 1999). Discuss. Math. Differ. Incl. Control Optim. 20. 195 207.
- STUDNIARSKI, M. and TAHA, A.W.A. (2003) Stability properties of weak sharp minima. Control Cybernet. 32, 351-359.
- STUDNIARSKI, M. and WARD, D.E. (1999) Weak sharp minima: characterizations and sufficient conditions. SIAM J. Control Optim. 38, 219-236.
- WARD, D.E. (1994) Characterizations of strict local minima and necessary conditions for weak sharp minima. J. Optim. Theory Appl. 80, 551-571.
- 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 Programming with Data Perturbations, Led. Notes Pure Appl. Math., 195, Dekker, New York, 419-436.
- ZHENG, X.Y., YANG, X.M. and TEO, K.L. (2006) Sharp minima for multiobjective optimization in Banach spaces, Set-Valued Anal. 14, 327-345.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0026-0007