Muutke küpsiste eelistusi

E-raamat: Optimality Conditions in Convex Optimization: A Finite-Dimensional View

(NSHM, Durgapur),
  • Formaat: 444 pages
  • Ilmumisaeg: 17-Oct-2011
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781040157695
Teised raamatud teemal:
  • Formaat - EPUB+DRM
  • Hind: 100,09 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Optimality Conditions in Convex Optimization: A Finite-Dimensional ViewSuurem pilt
  • Formaat: 444 pages
  • Ilmumisaeg: 17-Oct-2011
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781040157695
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

Optimality Conditions in Convex Optimization explores an important and central issue in the field of convex optimization: optimality conditions. It brings together the most important and recent results in this area that have been scattered in the literaturenotably in the area of convex analysisessential in developing many of the important results in this book, and not usually found in conventional texts. Unlike other books on convex optimization, which usually discuss algorithms along with some basic theory, the sole focus of this book is on fundamental and advanced convex optimization theory.

Although many results presented in the book can also be proved in infinite dimensions, the authors focus on finite dimensions to allow for much deeper results and a better understanding of the structures involved in a convex optimization problem. They address semi-infinite optimization problems; approximate solution concepts of convex optimization problems; and some classes of non-convex problems which can be studied using the tools of convex analysis. They include examples wherever needed, provide details of major results, and discuss proofs of the main results.

Arvustused

"It discusses a number of major approaches to the subject, bringing together many results from the past thirty-five years into one handy volume. Researchers in variational analysis should find this book to be a useful reference; for those new to convex optimization, it provides a very accessible entry point to the field. I have begun recommending it to graduate students who would like to learn about convex subdifferential calculus. a valuable book, a most welcome addition to the optimization theory literature." Doug Ward, Mathematical Reviews, January 2013

List of Figures xi
Symbol Description xiii
Foreword xv
Preface xvii
1 What Is Convex Optimization? 1(22)
1.1 Introduction
1(1)
1.2 Basic Concepts
2(13)
1.3 Smooth Convex Optimization
15(8)
2 Tools for Convex Optimization 23(120)
2.1 Introduction
23(1)
2.2 Convex Sets
23(39)
2.2.1 Convex Cones
39(5)
2.2.2 Hyperplane and Separation Theorems
44(6)
2.2.3 Polar Cones
50(4)
2.2.4 Tangent and Normal Cones
54(6)
2.2.5 Polyhedral Sets
60(2)
2.3 Convex Functions
62(36)
2.3.1 Sublinear and Support Functions
71(4)
2.3.2 Continuity Property
75(10)
2.3.3 Differentiability Property
85(13)
2.4 Subdifferential Calculus
98(13)
2.5 Conjugate Functions
111(11)
2.6 E-Subdifferential
122(14)
2.7 Epigraphical Properties of Conjugate Functions
136(7)
3 Basic Optimality Conditions Using the Normal Cone 143(26)
3.1 Introduction
143(2)
3.2 Slater Constraint Qualification
145(9)
3.3 Abadie Constraint Qualification
154(3)
3.4 Convex Problems with Abstract Constraints
157(2)
3.5 Max-Function Approach
159(2)
3.6 Cone-Constrained Convex Programming
161(8)
4 Saddle Points, Optimality, and Duality 169(38)
4.1 Introduction
169(2)
4.2 Basic Saddle Point Theorem
171(4)
4.3 Afline Inequalities and Equalities and Saddle Point Condition
175(10)
4.4 Lagrangian Duality
185(11)
4.5 Fenchel Duality
196(4)
4.6 Equivalence between Lagrangian and Fenchel Duality
200(7)
5 Enhanced Fritz John Optimality Conditions 207(36)
5.1 Introduction
207(1)
5.2 Enhanced Fritz John Conditions Using the Subdifferential
208(8)
5.3 Enhanced Fritz John Conditions under Restrictions
216(8)
5.4 Enhanced Fritz John Conditions in the Absence of Optimal Solution
224(11)
5.5 Enhanced Dual Fritz John Optimality Conditions
235(8)
6 Optimality without Constraint Qualification 243(38)
6.1 Introduction
243(6)
6.2 Geometric Optimality Condition: Smooth Case
249(6)
6.3 Geometric Optimality Condition: Nonsmooth Case
255(19)
6.4 Separable Sublinear Case
274(7)
7 Sequential Optimality Conditions 281(34)
7.1 Introduction
281(1)
7.2 Sequential Optimality: Thibault's Approach
282(11)
7.3 Fenchel Conjugates and Constraint Qualification
293(15)
7.4 Applications to Bilevel Programming Problems
308(7)
8 Representation of the Feasible Set and KKT Conditions 315(12)
8.1 Introduction
315(1)
8.2 Smooth Case
315(5)
8.3 Nonsmooth Case
320(7)
9 Weak Sharp Minima in Convex Optimization 327(10)
9.1 Introduction
327(1)
9.2 Weak Sharp Minima and Optimality
328(9)
10 Approximate Optimality Conditions 337(28)
10.1 Introduction
337(1)
10.2 E-Subdifferential Approach
338(4)
10.3 Max-Function Approach
342(3)
10.4 E-Saddle Point Approach
345(5)
10.5 Exact Penalization Approach
350(5)
10.6 Ekeland's Variational Principle Approach
355(3)
10.7 Modified E-KKT Conditions
358(3)
10.8 Duality-Based Approach to E-Optimality
361(4)
11 Convex Semi-Infinite Optimization 365(38)
11.1 Introduction
365(1)
11.2 Sup-Function Approach
366(2)
11.3 Reduction Approach
368(6)
11.4 Lagrangian Regular Point
374(8)
11.5 Farkas-Minkowski Linearization
382(13)
11.6 Noncompact Scenario: An Alternate Approach
395(8)
12 Convexity in Nonconvex Optimization 403(10)
12.1 Introduction
403(1)
12.2 Maximization of a Convex Function
403(5)
12.3 Minimization of d.c. Functions
408(5)
Bibliography 413(10)
Index 423
Anulekha Dhara earned her Ph.d. in IIT Delhi and subsequently moved to IIT Kanpur for her post-doctoral studies. Currently, she is a post-doctoral fellow in Mathematics at the University of Avignon, France. Her main area of interest is optimization theory.

Joydeep Dutta is an Associate Professor of Mathematics at the Indian Institute of Technology, (IIT) Kanpur. His main area of interest is optimization theory and applications.
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97810401576956e.html
Märksõnad: