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Performance evaluation of nonlinear optimization methods via pairwise comparison and fuzzy numbers. (English) Zbl 0586.90073

Discussed is a problem of performance evaluation of nonlinear optimization methods with the aid of a generalized pairwise comparison algorithm using fuzzy numbers. Its essence lies in representing the results of pairwise comparisons of the optimization methods in terms of triangular fuzzy numbers \((a_ i,b_ i,c_ i)\) with \(a_ i\), \(b_ i\) being lower and upper value, respectively, and \(b_ i\) denoting a modal value of the evaluation of the i-th optimization method. This way of performance evaluation is applied to the following methods: 1) reduced gradient, 2) penalty function, 3) augmented Langrangian, 4) geometric programming. The methods are evaluated in the light of a set of criteria: 1) domain of applications, 2) robustness, 3) efficiency, 4) capacity, 5) conceptual simplicity, 6) shortness of code.
Reviewer: W.Pedrycz

MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
49M37 Numerical methods based on nonlinear programming
03E72 Theory of fuzzy sets, etc.
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