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- W2105598547 abstract "The paper addresses the tolerance approach to the sensitivity analysis of optimal solutions to the nonlinear optimization problem of the form $$mbox{$bigopluslimits_{yin S}C(y)tomin$quad overquad $Sinmathcal{S}$,}$$ where $mathcal{S}$ is a collection of nonempty subsets of a finite set $X$ such that the union of $mathcal{S}$ is $X$ and the intersection of $mathcal{S}$ is empty, $C$ is a cost (or weight) function from $X$ into $mathbb{R}^+=[0,infty)$ or $(0,infty)$, and $oplus$ is a continuous, associative, commutative, nondecreasing and unbounded binary operation of generalized addition on $mathbb{R}^+$, called an A-operation. We evaluate and present sharp estimates for upper and lower bounds of costs of elements from $X$, for which an optimal solution to the above problem remains stable. These bounds present new results in the sensitivity analysis as well as extend most known results in a unified way. We define an invariant of the optimization problem---the tolerance function, which is independent of optimal solutions, and establish its basic properties, among which we mention a characterization of the set of all optimal solutions, the uniqueness of optimal solutions and extremal values of the tolerance function on an optimal solution." @default.
- W2105598547 created "2016-06-24" @default.
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- W2105598547 date "2015-02-12" @default.
- W2105598547 modified "2023-09-27" @default.
- W2105598547 title "Stability Analysis in Discrete Optimization Involving Generalized Addition Operations" @default.
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- W2105598547 doi "https://doi.org/10.1007/s10957-015-0709-9" @default.
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