Adaptive thresholding technique for solving optimization problems on attainable sets of (max, min)-linear systems
Kybernetika (2018)
- Volume: 54, Issue: 2, page 400-412
- ISSN: 0023-5954
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topGad, Mahmoud. "Adaptive thresholding technique for solving optimization problems on attainable sets of (max, min)-linear systems." Kybernetika 54.2 (2018): 400-412. <http://eudml.org/doc/294496>.
@article{Gad2018,
abstract = {This article develops a parametric method depend on threshold technique for solving some optimization problems on attainable sets of so called (max, min)-separable linear systems. The concept of attainable set for (max, min)-separable linear equation systems will be introduced. Properties of the attainable sets will be studied in detail. The (max, min) - separable linear equation systems, in which the function of unknown variable occur only on one side, will be consider. The main idea of the proposed algorithm is that we will begin the calculations with the maximum element and we will try to decrease the value of the objective function of our problem, by decreasing its components in such a way that they stay within attainable set. Optimization problem consisting in finding the nearest point of an attainable set to a given fixed point will be considered. An algorithm for solving the optimization problem will be proposed. Motivational example from the area of operations research, which shows possible applications of the optimization problem solved in this paper, will be given. Numerical example illustrating the proposed algorithm is included.},
author = {Gad, Mahmoud},
journal = {Kybernetika},
keywords = {attainable sets; adaptive thresholding technique; (max; min)-separable equations},
language = {eng},
number = {2},
pages = {400-412},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Adaptive thresholding technique for solving optimization problems on attainable sets of (max, min)-linear systems},
url = {http://eudml.org/doc/294496},
volume = {54},
year = {2018},
}
TY - JOUR
AU - Gad, Mahmoud
TI - Adaptive thresholding technique for solving optimization problems on attainable sets of (max, min)-linear systems
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 2
SP - 400
EP - 412
AB - This article develops a parametric method depend on threshold technique for solving some optimization problems on attainable sets of so called (max, min)-separable linear systems. The concept of attainable set for (max, min)-separable linear equation systems will be introduced. Properties of the attainable sets will be studied in detail. The (max, min) - separable linear equation systems, in which the function of unknown variable occur only on one side, will be consider. The main idea of the proposed algorithm is that we will begin the calculations with the maximum element and we will try to decrease the value of the objective function of our problem, by decreasing its components in such a way that they stay within attainable set. Optimization problem consisting in finding the nearest point of an attainable set to a given fixed point will be considered. An algorithm for solving the optimization problem will be proposed. Motivational example from the area of operations research, which shows possible applications of the optimization problem solved in this paper, will be given. Numerical example illustrating the proposed algorithm is included.
LA - eng
KW - attainable sets; adaptive thresholding technique; (max; min)-separable equations
UR - http://eudml.org/doc/294496
ER -
References
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- Gad, M., Jablonský, J., Zimmermann, K., Incorrectly posed optimization problems under extremally linear equation constraints., In: Proc. 34th International Conference of Mathematical Methods in Economics MME 2016, Liberec 2016, pp. 231-236.
- Gavalec, M., Gad, M., Zimmermann, K., 10.1007/s10958-013-1492-5, J. Math. Sci. 193 (2013), 5, 645-658. Translated from Russian Journal Fundamentalnaya i Prikladnaya Matematika(Fundamental and Applied Mathematics) 17 (2012), 6, 3-21. DOI10.1007/s10958-013-1492-5
- Zimmernann, K., Extremální algebra (in Czech)., Ekon. ústav ČSAV, Praha 1976.
- Zimmermann, K., Gad, M., Optimization problems under one-sided -linear constraints., In: Conference Presentation of Mathematics ICPM'11, Liberec 2011, pp. 159-165.
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