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Numerical Optimization [electronic resource] : Theoretical and Practical Aspects / by J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal.

By: Bonnans, J. Frédéric [author.].
Contributor(s): Gilbert, J. Charles [author.] | Lemaréchal, Claude [author.] | Sagastizábal, Claudia A [author.] | SpringerLink (Online service).
Material type: TextTextSeries: Universitext: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006Description: XIV, 494 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540354475.Subject(s): Mathematical optimization | Numerical analysis | Computer software | Computer science | Optimization | Operations Research, Management Science | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | Algorithm Analysis and Problem Complexity | Mathematics of ComputingAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 519.6 Online resources: Click here to access online
Contents:
Unconstrained Problems -- General Introduction -- Basic Methods -- Line-Searches -- Newtonian Methods -- Conjugate Gradient -- Special Methods -- A Case Study: Seismic Reection Tomography -- Nonsmooth Optimization -- to Nonsmooth Optimization -- Some Methods in Nonsmooth Optimization -- Bundle Methods. The Quest for Descent -- Applications of Nonsmooth Optimization -- Computational Exercises -- Newton's Methods in Constrained Optimization -- Background -- Local Methods for Problems with Equality Constraints -- Local Methods for Problems with Equality and InequalityConstraints -- Exact Penalization -- Globalization by Line-Search -- Quasi-Newton Versions -- Interior-Point Algorithms for Linear and QuadraticOptimization -- Linearly Constrained Optimization and SimplexAlgorithm -- Linear Monotone Complementarity and Associated Vector Fields -- Predictor-Corrector Algorithms -- Non-Feasible Algorithms -- Self-Duality -- One-Step Methods -- Complexity of Linear Optimization Problems with Integer Data -- Karmarkar's Algorithm.
In: Springer eBooksSummary: Just as in its 1st edition, this book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. Most of the algorithms are explained in a detailed manner, allowing straightforward implementation. Theoretical aspects of the approaches chosen are also addressed with care, often using minimal assumptions. This new edition contains computational exercises in the form of case studies which help understanding optimization methods beyond their theoretical, description, when coming to actual implementation. Besides, the nonsmooth optimization part has been substantially reorganized and expanded.
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Unconstrained Problems -- General Introduction -- Basic Methods -- Line-Searches -- Newtonian Methods -- Conjugate Gradient -- Special Methods -- A Case Study: Seismic Reection Tomography -- Nonsmooth Optimization -- to Nonsmooth Optimization -- Some Methods in Nonsmooth Optimization -- Bundle Methods. The Quest for Descent -- Applications of Nonsmooth Optimization -- Computational Exercises -- Newton's Methods in Constrained Optimization -- Background -- Local Methods for Problems with Equality Constraints -- Local Methods for Problems with Equality and InequalityConstraints -- Exact Penalization -- Globalization by Line-Search -- Quasi-Newton Versions -- Interior-Point Algorithms for Linear and QuadraticOptimization -- Linearly Constrained Optimization and SimplexAlgorithm -- Linear Monotone Complementarity and Associated Vector Fields -- Predictor-Corrector Algorithms -- Non-Feasible Algorithms -- Self-Duality -- One-Step Methods -- Complexity of Linear Optimization Problems with Integer Data -- Karmarkar's Algorithm.

Just as in its 1st edition, this book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. Most of the algorithms are explained in a detailed manner, allowing straightforward implementation. Theoretical aspects of the approaches chosen are also addressed with care, often using minimal assumptions. This new edition contains computational exercises in the form of case studies which help understanding optimization methods beyond their theoretical, description, when coming to actual implementation. Besides, the nonsmooth optimization part has been substantially reorganized and expanded.

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Other editions of this work

Numerical optimization by Bonnans J Frederic
Numerical optimization by Bonnans J Frederic
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