The Linearization Method for Constrained Optimization [electronic resource] /
Techniques of optimization are applied in many problems in economics, automatic control, engineering, etc. and a wealth of literature is devoted to this subject. The first computer applications involved linear programming problems with simp- le structure and comparatively uncomplicated nonlinear pro- blems: These could be solved readily with the computational power of existing machines, more than 20 years ago. Problems of increasing size and nonlinear complexity made it necessa- ry to develop a complete new arsenal of methods for obtai- ning numerical results in a reasonable time. The lineariza- tion method is one of the fruits of this research of the last 20 years. It is closely related to Newton's method for solving systems of linear equations, to penalty function me- thods and to methods of nondifferentiable optimization. It requires the efficient solution of quadratic programming problems and this leads to a connection with conjugate gra- dient methods and variable metrics. This book, written by one of the leading specialists of optimization theory, sets out to provide - for a wide readership including engineers, economists and optimization specialists, from graduate student level on - a brief yet quite complete exposition of this most effective method of solution of optimization problems.
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Format: | Texto biblioteca |
Language: | eng |
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Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,
1994
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Subjects: | Mathematics., System theory., Numerical analysis., Calculus of variations., Applied mathematics., Engineering mathematics., Economic theory., Systems Theory, Control., Calculus of Variations and Optimal Control; Optimization., Numerical Analysis., Appl.Mathematics/Computational Methods of Engineering., Economic Theory/Quantitative Economics/Mathematical Methods., |
Online Access: | http://dx.doi.org/10.1007/978-3-642-57918-9 |
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KOHA-OAI-TEST:1873722018-07-30T23:10:35ZThe Linearization Method for Constrained Optimization [electronic resource] / Pshenichnyj, Boris N. author. SpringerLink (Online service) textBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,1994.engTechniques of optimization are applied in many problems in economics, automatic control, engineering, etc. and a wealth of literature is devoted to this subject. The first computer applications involved linear programming problems with simp- le structure and comparatively uncomplicated nonlinear pro- blems: These could be solved readily with the computational power of existing machines, more than 20 years ago. Problems of increasing size and nonlinear complexity made it necessa- ry to develop a complete new arsenal of methods for obtai- ning numerical results in a reasonable time. The lineariza- tion method is one of the fruits of this research of the last 20 years. It is closely related to Newton's method for solving systems of linear equations, to penalty function me- thods and to methods of nondifferentiable optimization. It requires the efficient solution of quadratic programming problems and this leads to a connection with conjugate gra- dient methods and variable metrics. This book, written by one of the leading specialists of optimization theory, sets out to provide - for a wide readership including engineers, economists and optimization specialists, from graduate student level on - a brief yet quite complete exposition of this most effective method of solution of optimization problems.1. Convex and Quadratic Programming -- 1.1 Introduction -- 1.2 Necessary Conditions for a Minimum and Duality -- 1.3 Quadratic Programming Problems -- 2. The Linearization Method -- 2.1 The General Algorithm -- 2.2 Resolution of Systems of Equations and Inequalities -- 2.3 Acceleration of the Convergence of the Linearization Method -- 3. The Discrete Minimax Problem and Algorithms -- 3.1 The Discrete Minimax Problem -- 3.2 The Dual Algorithm for Convex Programming Problems -- 3.3 Algorithms and Examples -- Appendix: Comments on the Literature -- References.Techniques of optimization are applied in many problems in economics, automatic control, engineering, etc. and a wealth of literature is devoted to this subject. The first computer applications involved linear programming problems with simp- le structure and comparatively uncomplicated nonlinear pro- blems: These could be solved readily with the computational power of existing machines, more than 20 years ago. Problems of increasing size and nonlinear complexity made it necessa- ry to develop a complete new arsenal of methods for obtai- ning numerical results in a reasonable time. The lineariza- tion method is one of the fruits of this research of the last 20 years. It is closely related to Newton's method for solving systems of linear equations, to penalty function me- thods and to methods of nondifferentiable optimization. It requires the efficient solution of quadratic programming problems and this leads to a connection with conjugate gra- dient methods and variable metrics. This book, written by one of the leading specialists of optimization theory, sets out to provide - for a wide readership including engineers, economists and optimization specialists, from graduate student level on - a brief yet quite complete exposition of this most effective method of solution of optimization problems.Mathematics.System theory.Numerical analysis.Calculus of variations.Applied mathematics.Engineering mathematics.Economic theory.Mathematics.Systems Theory, Control.Calculus of Variations and Optimal Control; Optimization.Numerical Analysis.Appl.Mathematics/Computational Methods of Engineering.Economic Theory/Quantitative Economics/Mathematical Methods.Springer eBookshttp://dx.doi.org/10.1007/978-3-642-57918-9URN:ISBN:9783642579189 |
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Mathematics. System theory. Numerical analysis. Calculus of variations. Applied mathematics. Engineering mathematics. Economic theory. Mathematics. Systems Theory, Control. Calculus of Variations and Optimal Control; Optimization. Numerical Analysis. Appl.Mathematics/Computational Methods of Engineering. Economic Theory/Quantitative Economics/Mathematical Methods. Mathematics. System theory. Numerical analysis. Calculus of variations. Applied mathematics. Engineering mathematics. Economic theory. Mathematics. Systems Theory, Control. Calculus of Variations and Optimal Control; Optimization. Numerical Analysis. Appl.Mathematics/Computational Methods of Engineering. Economic Theory/Quantitative Economics/Mathematical Methods. |
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Mathematics. System theory. Numerical analysis. Calculus of variations. Applied mathematics. Engineering mathematics. Economic theory. Mathematics. Systems Theory, Control. Calculus of Variations and Optimal Control; Optimization. Numerical Analysis. Appl.Mathematics/Computational Methods of Engineering. Economic Theory/Quantitative Economics/Mathematical Methods. Mathematics. System theory. Numerical analysis. Calculus of variations. Applied mathematics. Engineering mathematics. Economic theory. Mathematics. Systems Theory, Control. Calculus of Variations and Optimal Control; Optimization. Numerical Analysis. Appl.Mathematics/Computational Methods of Engineering. Economic Theory/Quantitative Economics/Mathematical Methods. Pshenichnyj, Boris N. author. SpringerLink (Online service) The Linearization Method for Constrained Optimization [electronic resource] / |
description |
Techniques of optimization are applied in many problems in economics, automatic control, engineering, etc. and a wealth of literature is devoted to this subject. The first computer applications involved linear programming problems with simp- le structure and comparatively uncomplicated nonlinear pro- blems: These could be solved readily with the computational power of existing machines, more than 20 years ago. Problems of increasing size and nonlinear complexity made it necessa- ry to develop a complete new arsenal of methods for obtai- ning numerical results in a reasonable time. The lineariza- tion method is one of the fruits of this research of the last 20 years. It is closely related to Newton's method for solving systems of linear equations, to penalty function me- thods and to methods of nondifferentiable optimization. It requires the efficient solution of quadratic programming problems and this leads to a connection with conjugate gra- dient methods and variable metrics. This book, written by one of the leading specialists of optimization theory, sets out to provide - for a wide readership including engineers, economists and optimization specialists, from graduate student level on - a brief yet quite complete exposition of this most effective method of solution of optimization problems. |
format |
Texto |
topic_facet |
Mathematics. System theory. Numerical analysis. Calculus of variations. Applied mathematics. Engineering mathematics. Economic theory. Mathematics. Systems Theory, Control. Calculus of Variations and Optimal Control; Optimization. Numerical Analysis. Appl.Mathematics/Computational Methods of Engineering. Economic Theory/Quantitative Economics/Mathematical Methods. |
author |
Pshenichnyj, Boris N. author. SpringerLink (Online service) |
author_facet |
Pshenichnyj, Boris N. author. SpringerLink (Online service) |
author_sort |
Pshenichnyj, Boris N. author. |
title |
The Linearization Method for Constrained Optimization [electronic resource] / |
title_short |
The Linearization Method for Constrained Optimization [electronic resource] / |
title_full |
The Linearization Method for Constrained Optimization [electronic resource] / |
title_fullStr |
The Linearization Method for Constrained Optimization [electronic resource] / |
title_full_unstemmed |
The Linearization Method for Constrained Optimization [electronic resource] / |
title_sort |
linearization method for constrained optimization [electronic resource] / |
publisher |
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, |
publishDate |
1994 |
url |
http://dx.doi.org/10.1007/978-3-642-57918-9 |
work_keys_str_mv |
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