This lecture note is intended for use in the course 04212 Optimization and Data Fitting at the Technincal University of Denmark. It covers about 25 of the curriculum. Hopefully, the note may be useful also to interested persons not participating in that course. The aim of the note is to give a n i n troduction to algorithms for unconstrained optimization. We present Conjugate Gradient, Damped Newton and Quasi Newton methods together with the relevant theoretical background. The reader is

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... to be familiar with algorithms for solving linear and nonlinear system of equations, at a level corresponding to an introductory course in numerical analysis. The algorithms presented in the note appear in any g o o d p r ogram library, and implementations can be found via GAMS Guide to Available Mathematical Software at the Internet address http: gams.nist.gov The examples in the note were computed in Matlab. The programs are available via