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Introduction to continuous optimization

Polyak, Roman A.

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Introduction to continuous optimization

Record Type:	Electronic resources : Monograph/item
Title/Author:	Introduction to continuous optimization/ by Roman A. Polyak.
Author:	Polyak, Roman A.
Published:	Cham :Springer International Publishing : : 2021.,
Description:	xvi, 541 p. :ill., digital ;24 cm.
[NT 15003449]:	1. Introduction -- 2. Elements of Calculus and Convex Analysis -- 3. Few Topics in Unconstrained Optimization -- 4. Optimization with Equality Constraints -- 5. Basics in Linear and Convex Optimization -- Self-Concordant Functions and IPM Complexity -- 7. Nonlinear Rescaling. Theory and Methods -- 8. Realizations of the NR Principle -- 9. Lagrangian Transformation and Interior Ellipsoid Methods -- 10. Finding Nonlinear Equilibrium -- 11. Applications and Numerical Results -- Concluding Remarks -- Appendix -- References.
Contained By:	Springer Nature eBook
Subject:	Mathematical optimization. -
Online resource:	https://doi.org/10.1007/978-3-030-68713-7
ISBN:	9783030687137

Introduction to continuous optimization
Polyak, Roman A.

Introduction to continuous optimization[electronic resource] /by Roman A. Polyak. - Cham :Springer International Publishing :2021. - xvi, 541 p. :ill., digital ;24 cm. - Springer optimization and its applications,v.1721931-6828 ;. - Springer optimization and its applications ;v.172..

1. Introduction -- 2. Elements of Calculus and Convex Analysis -- 3. Few Topics in Unconstrained Optimization -- 4. Optimization with Equality Constraints -- 5. Basics in Linear and Convex Optimization -- Self-Concordant Functions and IPM Complexity -- 7. Nonlinear Rescaling. Theory and Methods -- 8. Realizations of the NR Principle -- 9. Lagrangian Transformation and Interior Ellipsoid Methods -- 10. Finding Nonlinear Equilibrium -- 11. Applications and Numerical Results -- Concluding Remarks -- Appendix -- References.

This self-contained monograph presents the reader with an authoritative view of Continuous Optimization, an area of mathematical optimization that has experienced major developments during the past 40 years. The book contains results which have not yet been covered in a systematic way as well as a summary of results on NR theory and methods developed over the last several decades. The readership is aimed to graduate students in applied mathematics, computer science, economics, as well as researchers working in optimization and those applying optimization methods for solving real life problems. Sufficient exercises throughout provide graduate students and instructors with practical utility in a two-semester course in Continuous Optimization. The topical coverage includes interior point methods, self-concordance theory and related complexity issues, first and second order methods with accelerated convergence, nonlinear rescaling (NR) theory and exterior point methods, just to mention a few. The book contains a unified approach to both interior and exterior point methods with emphasis of the crucial duality role. One of the main achievements of the book shows what makes the exterior point methods numerically attractive and why. The book is composed in five parts. The first part contains the basics of calculus, convex analysis, elements of unconstrained optimization, as well as classical results of linear and convex optimization. The second part contains the basics of self-concordance theory and interior point methods, including complexity results for LP, QP, and QP with quadratic constraint, semidefinite and conic programming. In the third part, the NR and Lagrangian transformation theories are considered and exterior point methods are described. Three important problems in finding equilibrium are considered in the fourth part. In the fifth and final part of the book, several important applications arising in economics, structural optimization, medicine, statistical learning theory, and more, are detailed. Numerical results, obtained by solving a number of real life and test problems, are also provided.

ISBN: 9783030687137

Standard No.: 10.1007/978-3-030-68713-7doiSubjects--Topical Terms:

517763
Mathematical optimization.

LC Class. No.: QA402.5 / .P659 2021

Dewey Class. No.: 519.6

Introduction to continuous optimization
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100 1 $a Polyak, Roman A. $3 3494763
245 1 0 $a Introduction to continuous optimization $h [electronic resource] / $c by Roman A. Polyak.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
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490 1 $a Springer optimization and its applications, $x 1931-6828 ; $v v.172
505 0 $a 1. Introduction -- 2. Elements of Calculus and Convex Analysis -- 3. Few Topics in Unconstrained Optimization -- 4. Optimization with Equality Constraints -- 5. Basics in Linear and Convex Optimization -- Self-Concordant Functions and IPM Complexity -- 7. Nonlinear Rescaling. Theory and Methods -- 8. Realizations of the NR Principle -- 9. Lagrangian Transformation and Interior Ellipsoid Methods -- 10. Finding Nonlinear Equilibrium -- 11. Applications and Numerical Results -- Concluding Remarks -- Appendix -- References.
520 $a This self-contained monograph presents the reader with an authoritative view of Continuous Optimization, an area of mathematical optimization that has experienced major developments during the past 40 years. The book contains results which have not yet been covered in a systematic way as well as a summary of results on NR theory and methods developed over the last several decades. The readership is aimed to graduate students in applied mathematics, computer science, economics, as well as researchers working in optimization and those applying optimization methods for solving real life problems. Sufficient exercises throughout provide graduate students and instructors with practical utility in a two-semester course in Continuous Optimization. The topical coverage includes interior point methods, self-concordance theory and related complexity issues, first and second order methods with accelerated convergence, nonlinear rescaling (NR) theory and exterior point methods, just to mention a few. The book contains a unified approach to both interior and exterior point methods with emphasis of the crucial duality role. One of the main achievements of the book shows what makes the exterior point methods numerically attractive and why. The book is composed in five parts. The first part contains the basics of calculus, convex analysis, elements of unconstrained optimization, as well as classical results of linear and convex optimization. The second part contains the basics of self-concordance theory and interior point methods, including complexity results for LP, QP, and QP with quadratic constraint, semidefinite and conic programming. In the third part, the NR and Lagrangian transformation theories are considered and exterior point methods are described. Three important problems in finding equilibrium are considered in the fourth part. In the fifth and final part of the book, several important applications arising in economics, structural optimization, medicine, statistical learning theory, and more, are detailed. Numerical results, obtained by solving a number of real life and test problems, are also provided.
650 0 $a Mathematical optimization. $3 517763
650 1 4 $a Continuous Optimization. $3 1566748
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