Titlebook: Numerical Optimization; Theoretical and Prac J. Frédéric Bonnans,J. Charles Gilbert,Claudia A. Textbook 20031st edition Springer-Verlag Be

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J. Frédéric Bonnans,J. Charles Gilbert,Claudia A. Combines mathematical developments, description and analysis of algorithms.Selection of algorithms is based on their applicability to real-life problems.Includes supplementary material:

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General Introductiont will be the usual dot-product: .); | · | or ∥ · ∥ will denote the associated norm. The . (vector of partial derivatives) of a function .: ℝ. → ℝ will be denoted by ∇ . or .′; the . (matrix of second derivatives) by ∇.. or .″. We will also use continually the notation .(.) = .′(.).

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Special Methodsmely important, and might supersede line-searches, sooner or later. The other methods deal with the direction; they are either classical (Gauss-Newton) or recent (limited-memory quasi-Newton, truncated Newton) and apply only in some well-defined subclasses of problems.

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Bundle Methods. The Quest of DescentNone of the black-box methods considered so far are descent schemes. Only the steepest-descent method guarantees a decrease of the objective function at each iteration. However, it requires the complete knowledge of .., and can be unstable.

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