連続最適化入門 Introduction to Continuous Optimization (Springer Optimization and Its Applications)

連続最適化入門<br>Introduction to Continuous Optimization (Springer Optimization and Its Applications)

個数：

ポイントキャンペーン

連続最適化入門
Introduction to Continuous Optimization (Springer Optimization and Its Applications)

Polyak, Roman A.

ウェブストア価格 ¥34,690（本体¥31,537）
Springer Nature Switzerland AG（2021/04発売）
外貨定価 US$ 159.99
【ウェブストア限定】洋書・洋古書ポイント5倍対象商品（～2/28）
ポイント 1,575pt

提携先の海外書籍取次会社に在庫がございます。通常3週間で発送いたします。
【重要ご説明事項】
1. 納期遅延や、ご入手不能となる場合が若干ございます。
2. 複数冊ご注文の場合は、ご注文数量が揃ってからまとめて発送いたします。
3. 美品のご指定は承りかねます。

●3Dセキュア導入とクレジットカードによるお支払いについて

【入荷遅延について】
世界情勢の影響により、海外からお取り寄せとなる洋書・洋古書の入荷が、表示している標準的な納期よりも遅延する場合がございます。
おそれいりますが、あらかじめご了承くださいますようお願い申し上げます。

◆画像の表紙や帯等は実物とは異なる場合があります。

◆ウェブストアでの洋書販売価格は、弊社店舗等での販売価格とは異なります。
また、洋書販売価格は、ご注文確定時点での日本円価格となります。
ご注文確定後に、同じ洋書の販売価格が変動しても、それは反映されません。

製本 Hardcover:ハードカバー版／ページ数 541 p.
言語 ENG
商品コード 9783030687113

Full Description

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.

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. (With Igor Griva) Applications and Numerical Results.- Concluding Remarks.- Appendix.- References.