Muutke küpsiste eelistusi

E-raamat: Optimization on Metric and Normed Spaces

Teised raamatud teemal:
  • Formaat - PDF+DRM
  • Hind: 110,53 €*
  • * 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.
Optimization on Metric and Normed SpacesSuurem pilt
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. 

"Optimization on Metric and Normed Spaces" is devoted to the recent progress in optimization on Banach spaces and complete metric spaces.Optimization problems are usually considered on metric spaces satisfying certain compactness assumptions which guarantee the existence of solutions and convergence of algorithms. This book considers spaces that do not satisfy such compactness assumptions. In order to overcome these difficulties, the book uses the Baire category approach and considers approximate solutions. Therefore, it presents a number of new results concerning penalty methods in constrained optimization, existence of solutions in parametric optimization, well-posedness of vector minimization problems, and many other results obtained in the last ten years.The book is intended for mathematicians interested in optimization and applied functional analysis.

Covering recent work on Banach and complete metric spaces, this book uses the Baire approach and considers approximate solutions. It presents new results including penalty methods in constrained optimization and extant solutions in parametric optimization.
Preface v
1 Introduction
1(10)
1.1 Penalty methods
1(5)
1.2 Generic existence of solutions of minimization problems
6(4)
1.3 Comments
10(1)
2 Exact Penalty in Constrained Optimization
11(70)
2.1 Problems with a locally Lipschitzian constraint function
11(4)
2.2 Proofs of Theorems 2.1-2.4
15(5)
2.3 An optimization problem in a finite-dimensional space
20(4)
2.4 Inequality-constrained problems with convex constraint functions
24(4)
2.5 Proof of Propositions 2.15, 2.17 and 2.18
28(4)
2.6 Proof of Theorem 2.11
32(4)
2.7 Optimization problems with mixed nonsmooth nonconvex constraints
36(7)
2.8 Proof of Theorem 2.22
43(5)
2.9 Optimization problems with smooth constraint and objective functions
48(4)
2.10 Proofs of Theorems 2.26 and 2.27
52(7)
2.11 Optimization problems in metric spaces
59(5)
2.12 Proof of Theorem 2.35
64(7)
2.13 An extension of Theorem 2.35
71(2)
2.14 Exact penalty property and Mordukhovich basic subdifferential
73(3)
2.15 Proofs of Theorems 2.40 and 2.41
76(3)
2.16 Comments
79(2)
3 Stability of the Exact Penalty
81(40)
3.1 Minimization problems with one constraint
81(5)
3.2 Auxiliary results
86(2)
3.3 Proof of Theorems 3.4 and 3.5
88(5)
3.4 Problems with convex constraint functions
93(5)
3.5 Proof of Theorem 3.12
98(4)
3.6 An extension of Theorem 3.12 for problems with one constraint function
102(2)
3.7 Proof of Theorem 3.14
104(3)
3.8 Nonconvex inequality-constrained minimization problems
107(5)
3.9 Proof of Theorem 3.16
112(8)
3.10 Comments
120(1)
4 Generic Well-Posedness of Minimization Problems
121(60)
4.1 A generic variational principle
121(2)
4.2 Two classes of minimization problems
123(1)
4.3 The generic existence result for problem (P1)
124(3)
4.4 The weak topology on the space M
127(4)
4.5 Proofs of Theorems 4.4 and 4.5
131(2)
4.6 An extension of Theorem 4.4
133(2)
4.7 The generic existence result for problem (P2)
135(3)
4.8 Proof of Theorem 4.19
138(3)
4.9 A generic existence result in optimization
141(1)
4.10 A basic lemma for Theorem 4.23
142(4)
4.11 An auxiliary result
146(1)
4.12 Proof of Theorem 4.23
147(1)
4.13 Generic existence of solutions for problems with constraints
148(1)
4.14 An auxiliary variational principle
148(5)
4.15 The generic existence result for problem (P3)
153(1)
4.16 Proof of Theorem 4.31
154(3)
4.17 The generic existence result for problem (P4)
157(2)
4.18 Proof of Theorem 4.33
159(2)
4.19 Well-posedness of a class of minimization problems
161(3)
4.20 Auxiliary results for Theorems 4.36 and 4.37
164(2)
4.21 Auxiliary results for Theorem 4.38
166(2)
4.22 Proofs of Theorems 4.36 and 4.37
168(2)
4.23 Proof of Theorem 4.38
170(2)
4.24 Generic well-posedness for a class of equilibrium problems
172(2)
4.25 An auxiliary density result
174(2)
4.26 A perturbation lemma
176(2)
4.27 Proof of Theorem 4.48
178(2)
4.28 Comments
180(1)
5 Well-Posedness and Porosity
181(44)
5.1 σ-porous sets in a metric space
181(2)
5.2 Well-posedness of optimization problems
183(3)
5.3 A variational principle
186(4)
5.4 Well-posedness and porosity for classes of minimization problems
190(2)
5.5 Well-posedness and porosity in convex optimization
192(2)
5.6 Proof of Theorem 5.10
194(6)
5.7 A porosity result in convex minimization
200(1)
5.8 Auxiliary results for Theorem 5.12
201(2)
5.9 Proof of Theorem 5.12
203(2)
5.10 A porosity result for variational problems arising in crystallography
205(2)
5.11 The set M\ Mr is porous
207(1)
5.12 Auxiliary results
208(2)
5.13 Proof of Theorem 5.20
210(6)
5.14 Porosity results for a class of equlibrium problems
216(1)
5.15 The first porosity result
217(2)
5.16 The second porosity result
219(2)
5.17 The third porosity result
221(3)
5.18 Comments
224(1)
6 Parametric Optimization
225(42)
6.1 Generic variational principle
225(2)
6.2 Concretization of the hypothesis (H)
227(5)
6.3 Two generic existence results
232(5)
6.4 A generic existence result in parametric optimization
237(1)
6.5 Parametric optimization and porosity
238(1)
6.6 A variational principle and porosity
239(5)
6.7 Concretization of the variational principle
244(4)
6.8 Existence results for the problem (P2)
248(7)
6.9 Existence results for the problem (P1)
255(2)
6.10 Parametric optimization problems with constraints
257(2)
6.11 Proof of Theorem 6.25
259(6)
6.12 Comments
265(2)
7 Optimization with Increasing Objective Functions
267(44)
7.1 Preliminaries
267(1)
7.2 A variational principle
268(5)
7.3 Spaces of increasing coercive functions
273(1)
7.4 Proof of Theorem 7.4
274(3)
7.5 Spaces of increasing noncoercive functions
277(1)
7.6 Proof of Theorem 7.10
278(2)
7.7 Spaces of increasing quasiconvex functions
280(1)
7.8 Proof of Theorem 7.14
281(5)
7.9 Spaces of increasing convex functions
286(2)
7.10 Proof of Theorem 7.21
288(1)
7.11 The generic existence result for the minimization problem (P2)
289(2)
7.12 Proofs of Theorems 7.29 and 7.30
291(4)
7.13 Well-posedness of optimization problems with increasing cost functions
295(3)
7.14 Variational principles
298(5)
7.15 Spaces of increasing functions
303(6)
7.16 Comments
309(2)
8 Generic Well-Posedness of Minimization Problems with Constraints
311(38)
8.1 Variational principles
311(2)
8.2 Proof of Proposition 8.2
313(4)
8.3 Minimization problems with mixed continuous constraints
317(3)
8.4 An auxiliary result for (A2)
320(1)
8.5 An auxiliary result for (A3)
321(1)
8.6 An auxiliary result for (A4)
322(5)
8.7 Proof of Theorems 8.4 and 8.5
327(1)
8.8 An abstract implicit function theorem
328(1)
8.9 Proof of Theorem 8.10
329(4)
8.10 An extension of the classical implicit function
333(3)
8.11 Minimization problems with mixed smooth constraints
336(2)
8.12 Auxiliary results
338(3)
8.13 An auxiliary result for hypothesis (A4)
341(5)
8.14 Proof of Theorems 8.15 and 8.16
346(1)
8.15 Comments
347(2)
9 Vector Optimization
349(46)
9.1 Generic and density results in vector optimization
349(1)
9.2 Proof of Proposition 9.1
350(2)
9.3 Auxiliary results
352(8)
9.4 Proof of Theorem 9.2
360(1)
9.5 Proof of Theorem 9.3
361(7)
9.6 Vector optimization with continuous objective functions
368(2)
9.7 Preliminaries
370(1)
9.8 Auxiliary results
371(6)
9.9 Proof of Theorem 9.9
377(4)
9.10 Vector optimization with semicontinuous objective functions
381(3)
9.11 Auxiliary results for Theorem 9.14
384(4)
9.12 Proof of Theorem 9.14
388(2)
9.13 Density results
390(4)
9.14 Comments
394(1)
10 Infinite Horizon Problems
395(32)
10.1 Minimal solutions for discrete-time control systems in metric spaces
395(2)
10.2 Auxiliary results
397(4)
10.3 Proof of Theorem 10.2
401(6)
10.4 Properties of good sequences
407(1)
10.5 Convex discrete-time control systems in a Banach space
408(2)
10.6 Preliminary results
410(3)
10.7 Proofs of Theorems 10.13 and 10.14
413(7)
10.8 Control systems on metric spaces
420(1)
10.9 Proof of Proposition 10.23
421(2)
10.10 An auxiliary result for Theorem 10.24
423(1)
10.11 Proof of Theorem 10.24
424(1)
10.12 Comments
425(2)
References 427(6)
Index 433
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97803878862132e.html
Märksõnad: