Abstract
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], Phu, Hoffmann and Hichert [8, 9, 10, 17] 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 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 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.
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