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Abstract. We propose performance profiles -distribution functions for a performance metric -as a tool for benchmarking and comparing optimization software. We show that performance profiles combine the best features of other tools for performance evaluation.

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This paper is an attempt to motivate and justify quasi-Newton methods as useful modifications of Newton's method for general and gradient nonlinear systems of equations. References are given to ample numerical justification; here we give an overview of many of the important theoretical results and each is accompanied by sufficient discussion to make the results and henc6 the methods plausible.