Muutke küpsiste eelistusi

Topological Aspects of Nonsmooth Optimization 2012 [Kõva köide]

  • Formaat: Hardback, 196 pages, kõrgus x laius: 235x155 mm, kaal: 483 g, XII, 196 p., 1 Hardback
  • Sari: Nonconvex Optimization and Its Applications 64
  • Ilmumisaeg: 17-Nov-2011
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1461418968
  • ISBN-13: 9781461418962
Teised raamatud teemal:
  • Kõva köide
  • Hind: 95,02 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Tavahind: 111,79 €
  • Säästad 15%
  • Raamatu kohalejõudmiseks kirjastusest kulub orienteeruvalt 2-4 nädalat
  • Kogus:
  • Lisa ostukorvi
  • Tasuta tarne
  • Tellimisaeg 2-4 nädalat
  • Lisa soovinimekirja
Topological Aspects of Nonsmooth Optimization 2012Suurem pilt
  • Formaat: Hardback, 196 pages, kõrgus x laius: 235x155 mm, kaal: 483 g, XII, 196 p., 1 Hardback
  • Sari: Nonconvex Optimization and Its Applications 64
  • Ilmumisaeg: 17-Nov-2011
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1461418968
  • ISBN-13: 9781461418962
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781461418962.html
Märksõnad:
Linking singularity and transversality theory with non-smooth optimization, this book examines complementarity-constrained mathematical programs, semi-infinite programming problems, mathematical programs with vanishing constraints, and bi-level optimization.

This book deals with nonsmooth structures arising within the optimization setting. It considers four optimization problems, namely, mathematical programs with complementarity constraints, general semi-infinite programming problems, mathematical programs with vanishing constraints and bilevel optimization. The author uses the topological approach and topological invariants of corresponding feasible sets are investigated. Moreover, the critical point theory in the sense of Morse is presented and parametric and stability issues are considered. The material progresses systematically and establishes a comprehensive theory for a rather broad class of optimization problems tailored to their particular type of nonsmoothness.  Topological Aspects of Nonsmooth Optimization will benefit researchers and graduate students in applied mathematics, especially those working in optimization theory, nonsmooth analysis, algebraic topology and singularity theory. ??

Arvustused

From the reviews:

This monograph provides detailed topological investigations of nonsmooth optimization problems. the book highlights and motivates recent developments in a broad field of active research. The material is well presented, so that the book may be warmly recommended to graduate students and researchers in optimization. (Oliver Stein, Mathematical Reviews, October, 2013)

The textbook (PhD thesis of the author) deals with mathematical programming problems which have smooth data but show, because of their structure, intrinsic non-smooth behavior . It can be used as a compendium of the critical-point theory also in the smooth case since nearly all important results are cited. New results are proved or it is referred to recently published results of the author. For researchers in the above described field of mathematical programming the book will become a very helpful and indispensable tool. (Armin Hoffmann, Zentralblatt MATH, Vol. 1234, 2012)

Preface vii
Notation xi
1 Introduction
1(14)
1.1 Nonsmooth optimization framework
1(2)
1.2 Topological approach
3(5)
1.3 Genericity and stability issues
8(1)
1.4 Nonlinear programming: smooth case
9(6)
2 Mathematical Programming Problems with Complementarity Constraints
15(48)
2.1 Applications and examples
15(3)
2.2 Stability and structure of the feasible set
18(22)
2.2.1 Constraint qualifications MFC and SMFC
19(11)
2.2.2 SMFC implies stability and Lipschitz manifold
30(10)
2.3 Critical point theory
40(12)
2.4 Parametric aspects
52(11)
3 General Semi-infinite Programming Problems
63(62)
3.1 Applications and examples
63(4)
3.2 Structure of the feasible set
67(30)
3.2.1 Closure of the feasible set and Sym-MFCQ
67(17)
3.2.2 Feasible set as a Lipschitz manifold
84(13)
3.3 Nonsmooth symmetric reduction ansatz
97(18)
3.4 Critical point theory
115(10)
4 Mathematical Programming Problems with Vanishing Constraints
125(16)
4.1 Applications and examples
125(2)
4.2 Critical point theory
127(14)
5 Bilevel Optimization
141(26)
5.1 Applications and examples
141(5)
5.2 Five types in parametric optimization
146(10)
5.3 Structure of the feasible set: dim(x) = 1
156(4)
5.4 Toward the case dim(x) ≥ 2
160(7)
6 Impacts on Nonsmooth Analysis
167(8)
6.1 Criticality for nonsmooth functions
167(1)
6.2 Versions of Sard's Theorem
168(4)
6.3 Regularity and implicit functions
172(3)
A Topology
175(4)
A.1 Cell attachment and deformation
175(1)
A.2 Whitney topology
176(3)
B Analysis
179(6)
B.1 Manifolds and implicit functions
179(2)
B.2 Transversality
181(4)
References 185(6)
Index 191