Milan Hladík. Global sensitivity analysis in optimization - the case of positive definite quadratic forms. In J. C. Figueroa-García and others, editors, Applied Computer Sciences in Engineering. WEA 2023, CCIS, pp. 265–275, Springer, Cham, 2023.
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We consider the problem of minimization of a positive definite quadratic form; this problem has a unique optimal solution. The question here is what are the largest allowable variations of the input data such that the optimal solution will not exceed given bounds? This problem is called global sensitivity analysis since, in contrast to the traditional sensitivity analysis, it deals with variations of possibly all input coefficients. We propose a general framework for approaching the problem with any matrix norm. We also focus on some commonly used norms and investigate for which of them the problem is efficiently solvable. Particularly for the max-norm, the problem is NP-hard, so we turn our attention to computationally cheap bounds.
@inCollection{Hla2023e,
author = "Milan Hlad\'{\i}k",
title = "Global sensitivity analysis in optimization - the case of positive definite quadratic forms",
editor = "J. C. Figueroa-Garc\'{\i}a and others",
feditor = "Juan Carlos Figueroa-Garc\'{\i}a and German Hern\'{a}ndez and Jose Luis Villa Ramirez and Elvis Eduardo Gaona Garc\'{\i}a",
booktitle = "Applied Computer Sciences in Engineering. WEA 2023",
booksubtitle = "10th Workshop on Engineering Applications, WEA 2023, Cartagena, Colombia, November 1-3, 2023, Proceedings",
publisher = "Springer",
address = "Cham",
series = "CCIS",
fseries = "Communications in Computer and Information Science",
volume = "1928",
pages = "265-275",
year = "2023",
doi = "10.1007/978-3-031-46739-4_24",
isbn = "978-3-031-46738-7",
issn = "1865-0929",
url = "https://doi.org/10.1007/978-3-031-46739-4_24",
bib2html_dl_html = "https://link.springer.com/chapter/10.1007/978-3-031-46739-4_24",
bib2html_dl_pdf = "https://rdcu.be/dqniT",
abstract = "We consider the problem of minimization of a positive definite quadratic form; this problem has a unique optimal solution. The question here is what are the largest allowable variations of the input data such that the optimal solution will not exceed given bounds? This problem is called global sensitivity analysis since, in contrast to the traditional sensitivity analysis, it deals with variations of possibly all input coefficients. We propose a general framework for approaching the problem with any matrix norm. We also focus on some commonly used norms and investigate for which of them the problem is efficiently solvable. Particularly for the max-norm, the problem is NP-hard, so we turn our attention to computationally cheap bounds.",
keywords = "Positive definiteness; Quadratic form; Sensitivity analysis; Tolerance analysis; Matrix norm; NP-hardness",
}
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