Approximation of set-valued functions by single-valued one
On robustness of set-valued maps and marginal value functions
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...
A primal-dual integral method in global optimization
Using the Fenchel conjugate of Phú’s Volume function F of a given essentially bounded measurable function f defined on the bounded box D ⊂ Rⁿ, the integral method of Chew and Zheng for global optimization is modified to a superlinearly convergent method with respect to the level sequence. Numerical results are given for low dimensional functions with a strict global essential supremum.
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