Milan Hladík. Optimal value bounds in nonlinear programming with interval data. TOP, 19(1):93–106, 2011.
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We consider nonlinear programming problems the input data of which are not fixed, but vary in some real compact intervals. The aim of this paper is to determine bounds of the optimal values. We propose a general framework for solving such problems. Under some assumption, the exact lower and upper bounds are computable by using two non-interval optimization problems. While these two optimization problems are hard to solve in general, we show that for some particular subclasses they can be reduced to easy problems. Subclasses that are considered are convex quadratic programming and posynomial geometric programming.
@article{Hla2011b,
author ="Milan Hlad\'{\i}k",
title = "Optimal value bounds in nonlinear programming with interval data",
journal = "TOP",
fjournal = "TOP: An Official Journal of the Spanish Society of Statistics and Operations Research",
pages = "93-106",
volume = "19",
number = "1",
year = "2011",
doi = "10.1007/s11750-009-0099-y",
url = "https://doi.org/10.1007/s11750-009-0099-y",
bib2html_dl_html = "http://dx.doi.org/10.1007/s11750-009-0099-y",
bib2html_dl_pdf = "https://rdcu.be/cnoUD",
abstract = "We consider nonlinear programming problems the input data of which are not fixed, but vary in some real compact intervals. The aim of this paper is to determine bounds of the optimal values. We propose a general framework for solving such problems. Under some assumption, the exact lower and upper bounds are computable by using two non-interval optimization problems. While these two optimization problems are hard to solve in general, we show that for some particular subclasses they can be reduced to easy problems. Subclasses that are considered are convex quadratic programming and posynomial geometric programming.",
}
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