On robustness of set-valued maps and marginal value functions

Armin Hoffmann; Abebe Geletu

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2005)

  • Volume: 25, Issue: 1, page 59-108
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Armin Hoffmann, and Abebe Geletu. "On robustness of set-valued maps and marginal value functions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 25.1 (2005): 59-108. <http://eudml.org/doc/271544>.

@article{ArminHoffmann2005,
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], 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.},
author = {Armin Hoffmann, Abebe Geletu},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
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-Fromovitz constraint qualification},
language = {eng},
number = {1},
pages = {59-108},
title = {On robustness of set-valued maps and marginal value functions},
url = {http://eudml.org/doc/271544},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Armin Hoffmann
AU - Abebe Geletu
TI - On robustness of set-valued maps and marginal value functions
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2005
VL - 25
IS - 1
SP - 59
EP - 108
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/271544
ER -

References

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