Convex analysis and minimization algorithms  1 ~ 2

Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal

From the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations...one of the strong features of these books...that they are designed not for the expert, but for those who whish to learn the subject matter starting from little or no background...there are numerous examples, and counter-examples, to back up the theory...To my knowledge, no other authors have given such a clear geometric account of convex analysis." "This innovative text is well written, copiously illustrated, and accessible to a wide audience"

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Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Minimization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to various fields related to optimization and operations research. These two topics making up the title of the book, reflect the two origins of the authors, who belong respectively to the academic world and to that of applications. Part I can be used as an introductory textbook (as a basis for courses, or for self-study); Part II continues this at a higher technical level and is addressed more to specialists, collecting results that so far have not appeared in books.

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[目次]

  • IX. Inner Construction of the Subdifferential.- X. Conjugacy in Convex Analysis.- XI. Approximate Subdifferentials of Convex Functions.- XII. Abstract Duality for Practitioners.- XIII. Methods of ?-Descent.- XIV. Dynamic Construction of Approximate Subdifferentials: Dual Form of Bundle Methods.- XV. Acceleration of the Cutting-Plane Algorithm: Primal Forms of Bundle Methods.- Bibliographical Comments.- References.

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[目次]

  • Table of Contents Part I.- I. Convex Functions of One Real Variable.- II. Introduction to Optimization Algorithms.- III. Convex Sets.- IV. Convex Functions of Several Variables.- V. Sublinearity and Support Functions.- VI. Subdifferentials of Finite Convex Functions.- VII. Constrained Convex Minimization Problems: Minimality Conditions, Elements of Duality Theory.- VIII. Descent Theory for Convex Minimization: The Case of Complete Information.- Appendix: Notations.- 1 Some Facts About Optimization.- 2 The Set of Extended Real Numbers.- 3 Linear and Bilinear Algebra.- 4 Differentiation in a Euclidean Space.- 5 Set-Valued Analysis.- 6 A Bird's Eye View of Measure Theory and Integration.- Bibliographical Comments.- References.

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この本の情報

書名 Convex analysis and minimization algorithms
著作者等 Hiriart-Urruty, Jean-Baptiste
Lemarechal, C.
Lemarechal Claude
シリーズ名 Die Grundlehren der mathematischen Wissenschaften
巻冊次 1
2
出版元 Springer-Verlag
刊行年月 c1993
版表示 1st ed. 1993. 2nd corr. printing 1996
ページ数 2 v.
大きさ 25 cm
ISBN 0387568506
0387568522
3540568522
3540568506
NCID BA21383444
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言語 英語
出版国 ドイツ
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