On robustness of set-valued maps and marginal value functions

• Autorzy: Armin Hoffmann , Abebe Geletu
• Języki publikacji: EN

Abstrakty

EN

The ideas of robust sets, robust functions and robustness of general set-valued maps were introduced by Chew and Zheng [7,26], and further developed by Shi, Zheng, Zhuang [18,19,20], Phú, Hoffmann and Hichert [8,9,10,17] to weaken up the semi-continuity requirements of certain global optimization algorithms. The robust analysis, along with the measure theory, has well served as the basis for the integral global optimization method (IGOM) (Chew and Zheng [7]). Hence, we have attempted to extend the robust analysis of Zheng et al. to that of robustness of set-valued maps with given structures and marginal value functions. We are also strongly convinced that the results of our investigation could open a way to apply the IGOM for the numerical treatment of some class of parametric optimization problems, when global optima are required.

Słowa kluczowe

EN

robust set; robust function; robust set-valued map; marginal value function; piecewise lower (upper) semi-continuous; approximatable function; approximatable set-valued map; regularity condition; extended Mangasarian-Fromovitz constraint qualification

Kategorie tematyczne

• 90C31: Sensitivity, stability, parametric optimization
• 49J53: Set-valued and variational analysis
• 90C34: Semi-infinite programming
• 49J52: Nonsmooth analysis

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2005
• Tom: 25
• Numer: 1
• Strony: 59-108

Daty

wydano

2005

otrzymano

2004-09-20

Twórcy

autor

Armin Hoffmann

• Technical University of Ilmenau, Institute of Mathematics, PF 100565, D98684 Ilmenau, Germany

autor

Abebe Geletu

• Technical University of Ilmenau, Institute of Mathematics, PF 100565, D98684 Ilmenau, Germany

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1059