Publikationen

The ideas of robust sets, robust functions and robustness of general set valued maps were introduced by Chew & Zheng and further developed by Shi, Zheng, Zhuang , Phú, Hoffmann and Hichert to weaken up the semi-continuity requirements of certain global optimization algorithms. Robust analysis, along with measure theory, has well served as the basis for the integral global optimization method (IGOM) (Chew & Zheng ). Hence, we have attempted here 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 of strong conviction 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. - MSC 2000: 90C34, 49J52, 49J53, 90C31. - Keywords: 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-Fromowitz constraint qualification.