Milan Hladík. Optimal value bounds in nonlinear programming with interval data. In Proceedings of the 20th international conference EURO Mini Conference: Continuous Optimization and Knowledge-Based Technologies, EurOPT 2008, May 20-23, Neringa, Lithunia, pp. 154–159, Technika, Vilnius, 2008.
We are concerned with nonlinear programming problems the input data in which vary in some real compact intervals. The question is to determine bounds of the optimal values. We present a general approach, where, under some assumption, the lower and upper bounds are computable by using two optimization problems. Even though 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.
@InProceedings{Hla2008da,
author = "Milan Hlad\'{\i}k",
title = "Optimal value bounds in nonlinear programming with interval data",
editor = "Sakalauskas, L. and Weber, G. W. and Zavadskas, E. K.",
booktitle = "Proceedings of the 20th international conference EURO Mini Conference: Continuous Optimization and Knowledge-Based Technologies, EurOPT 2008, May 20-23, Neringa, Lithunia",
pages = "154-159",
year = "2008",
publisher="Technika",
address="Vilnius",
bib2html_dl_pdf = "https://kam.mff.cuni.cz/~hladik/doc/2008-conf-EUROPT-OptValNLP.doc",
abstract = "We are concerned with nonlinear programming problems the input data in which vary in some real compact intervals. The question is to determine bounds of the optimal values. We present a general approach, where, under some assumption, the lower and upper bounds are computable by using two optimization problems. Even though 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.",
keywords = "interval systems, nonlinear programming, optimal value range, interval matrix",
}
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