Theory of linear optimization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Utrecht [u.a.]
VSP
2002
|
| Edition: | 1. publ. |
| Series: | Inverse and ill posed problems series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 241 - 248 |
| Physical Description: | VIII, 248 S. graph. Darst. : 25 cm |
| ISBN: | 906764353X |
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MARC
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| 100 | 1 | |a Eremin, Ivan I. |d 1933- |e Verfasser |0 (DE-588)123234603 |4 aut | |
| 245 | 1 | 0 | |a Theory of linear optimization |c I. I. Eremin |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Utrecht [u.a.] |b VSP |c 2002 | |
| 300 | |a VIII, 248 S. |b graph. Darst. : 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Inverse and ill posed problems series | |
| 500 | |a Literaturverz. S. 241 - 248 | ||
| 650 | 4 | |a Linear programming | |
| 650 | 4 | |a Convex programming | |
| 650 | 0 | 7 | |a Lineare Optimierung |0 (DE-588)4035816-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Optimierung |0 (DE-588)4035816-1 |D s |
| 689 | 0 | |5 DE-604 | |
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Record in the Search Index
| _version_ | 1808136531715555328 |
|---|---|
| adam_text |
CONTENTS
INTRODUCTION
1
CHAPTER
1.
FINITE
SYSTEMS
OF
LINEAR
INEQUALITIES
11
1.
BASIC
DEFINITIONS
.
11
2.
THE
STRUCTURE
OF
POLYHEDRONS
.
14
3.
BOUNDED
POLYHEDRONS
.
17
4.
A
PARAMETRIC
REPRESENTATION
OF
POLYHEDRONS
.
23
5.
THE
FARKAS-MINKOWSKI
THEOREM
ON
DEPENDENT
INEQUALITIES
.
27
6.
ATTAINABILITY
THEOREM
FOR
INEQUALITIES-IMPLICATIONS
OF
SECOND
KIND
.
32
7.
A
REFINED
FORMULATION
OF
THE
FARKAS-MINKOWSKI
THEOREM
.
34
8.
CONDITIONS
OF
COMPATIBILITY
OF
A
FINITE
SYSTEM
OF
LINEAR
INEQUALITIES
.
36
9.
THE
CLEANING
THEOREM
.
40
10.
SEPARABILITY
OF
NONINTERSECTING
POLYHEDRONS
.
40
11.
THE
FOURIER
ELIMINATION
METHOD
.
43
CHAPTER
2.
LINEAR
PROGRAMMING
47
12.
SETTING
OF
THE
PROBLEM
OF
LINEAR
PROGRAMMING
AND
SOME
ITS
PROPERTIES
47
13.
ECONOMIC
INTERPRETATION
OF
THE
LINEAR
PROGRAMMING
PROBLEM
.
49
14.
DUALITY:
INFORMATIVE
APPROACH
.
52
14.1.
THE
TWO-PERSON
GAME
WITH
ZERO
SUM
.
53
14.2.
THE
MODEL
"
PRODUCTION-MARKET
"
.
54
14.3.
THE
PLAY
APPROACH
TO
DUALITY
.
55
14.4.
THE
APPROACH
TO
DUALITY
WHERE
X
AND
U
IN
THE
LAGRANGE
FUNCTION
ARE
RENAMED
.
56
VI
14.5.
DUALITY
WHICH
FOLLOWS
FROM
THE
ANALYSIS
OF
THE
FARKAS
-
MINKOWSKI
THEOREM
.
58
14.6.
CONSTRUCTION
OF
THE
DUAL
PROBLEM
ON
THE
BASIS
OF
THERMO
DYNAMICAL
AXIOMATICS
.
59
15.
THE
DUALITY
THEOREM
.
60
16.
THE
OPTIMALITY
CONDITIONS
.
64
17.
INFORMATIVE
INTERPRETATION
OF
OPTIMALITY
CONDITIONS
.
67
18.
MATRIX
PLAYS
AND
DUALITY
.
68
19.
THE
THEOREM
ON
MARGINAL
VALUES
.
72
20.
THE
METHOD
OF
EXACT
PENALTY
FUNCTIONS
IN
LINEAR
PROGRAMMING
.
74
21.
LP
PROBLEMS
WITH
SEVERAL
CRITERION
FUNCTIONS
.
78
21.1.
THE
PARETO
OPTIMIZATION
MODEL
.
79
21.2.
THE
MODEL
OF
LEXICOGRAPHIC
(SUCCESSIVE)
OPTIMIZATION
.
82
CHAPTER
3.
INCONSISTENT
PROBLEMS
OF
LINEAR
PROGRAMMING
87
22.
CLASSIFICATION
OF
IMPROPER
PROBLEMS
OF
LINEAR
PROGRAMMING
(IP
LP)
87
23.
INFORMATIVE
INTERPRETATION
OF
IMPROPER
PROBLEMS
OF
LINEAR
PROGRAM
MING
.
90
24.
METHODS
OF
CORRECTION
OF
IMPROPER
PROBLEMS
OF
LINEAR
PROGRAMMING:
GENERAL
APPROACHES
.
94
24.1.
CORRECTION
OF
AN
IMPROPER
PROBLEM
OF
LINEAR
PROGRAMMING
BY
ITS
INFORMATIVE
COMPONENT
.
95
24.2.
OTHER
METHODS
OF
OPTIMAL
CORRECTION
.
97
25.
DUALITY:
THE
MAIN
THEOREM
.
99
25.1.
THE
SCHEME
OF
FORMING
A
PAIR
OF
MUTUALLY
DUAL
PROBLEMS
C
AND
(7*
CORRESPONDING
TO
THE
CASE
OF
AN
IMPROPER
PROBLEM
L
.
99
25.2.
MAIN
THEOREM
.
102
25.3.
COROLLARIES
FROM
THE
MAIN
THEOREM
.
109
26.
SPECIAL
REALIZATIONS
OF
DUALITY
.
110
27.
THE
DUALITY
THEOREM
FOR
/-PROBLEMS
.
114
CHAPTER
4.
PROBLEMS
OF
SUCCESSIVE
LINEAR
PROGRAMMING
AND
DUALITY
117
28.
THE
SCHEME
OF
DUALITY
FORMATION
IN
LINEAR
SUCCESSIVE
PROGRAMMING
119
29.
SOLVABILITY
CONDITIONS
FOR
LEXICOGRAPHIC
OPTIMIZATION
PROBLEMS
.
121
30.
THE
DUALITY
THEOREM
.
124
CONTENTS
VII
31.
REDUCTION
OF
LEXICOGRAPHIC
OPTIMIZATION
PROBLEMS
TO
SYSTEMS
OF
LINEAR
INEQUALITIES
.
125
31.1.
A
SCHEME
OF
REDUCTION
FOR
THE
TWO-STEP
OPTIMIZATION
PROBLEML26
31.2.
GENERAL
THEOREM
ON
REDUCIBILITY
.
127
32.
LEXICOGRAPHIC
DUALITY
FOR
IMPROPER
LP
PROBLEMS
-
A
SPECIAL
CASE
.
127
33.
DUALITY
FOR
IMPROPER
LP
PROBLEMS
IN
LEXICOGRAPHIC
INTERPRETATION
.
130
34.
SYMMETRIC
DUALITY
FOR
THE
PARETO
OPTIMIZATION
PROBLEM
.
134
CHAPTER
5.
STABILITY
AND
WELL-POSEDNESS
OF
LINEAR
PROGRAMMING
PROBLEMS
137
35.
NECESSARY
DEFINITIONS
AND
AUXILIARY
RESULTS
.
137
36.
STABILITY
OF
THE
LINEAR
PROGRAMMING
PROBLEM
.
147
37.
WELL-POSEDNESS
OF
LINEAR
PROGRAMMING
PROBLEMS
.
151
38.
THE
TIKHONOV
REGULARIZATION
OF
LINEAR
PROGRAMMING
PROBLEMS
.
.
.
152
38.1.
GEOMETRIC
SENSE
OF
THE
TIKHONOV
REGULARIZATION
.
153
38.2.
AN
AUXILIARY
LEMMA
.
154
38.3.
TIKHONOV
REGULARIZATION
OF
IMPROPER
LINEAR
PROGRAMMING
PROBLEMS
.
155
38.4.
STABLE
UNSOLVABILITY
OF
LP
PROBLEMS
.
157
38.5.
CONJUNCTION
OF
THE
TIKHONOV
REGULARIZATION
METHODS
AND
SQUARE
PENALTY
FUNCTIONS
.
159
CHAPTER
6.
METHODS
OF
PROJECTION
IN
LINEAR
PROGRAMMING
167
39.
FEJER
MAPPINGS
AND
THEIR
PROPERTIES
.
167
40.
BASIC
CONSTRUCTIONS
OF
FEJER
MAPPINGS
FOR
ALGEBRAIC
POLYHEDRONS
.
171
40.1.
SPECIAL
CONSTRUCTIONS
OF
FEJER
MAPPINGS
.
172
40.2.
GENERAL
REALIZATIONS
.
174
40.3.
THE
CONVERGENCE
THEOREM
.
175
40.4.
CONVERGENCE
RATE
OF
FEJER
PROCESSES
.
175
41.
DECOMPOSITION
AND
PARALLELIZING
OF
FEJER
PROCESSES
.
177
42.
RANDOMIZATION
OF
FEJER
PROCESSES
.
183
43.
FEJER
PROCESSES
AND
INCONSISTENT
SYSTEMS
OF
LINEAR
INEQUALITIES
.
.
.
186
43.1.
NONEXPANDING
M-FEJER
MAPPINGS
.
186
43.2.
THE
FEJER
PROCESS
FOR
THE
PROBLEM
OF
SQUARE
APPROXIMATION
OF
AN
INCOMPATIBLE
SYSTEM
OF
LINEAR
INEQUALITIES
.
190
43.3.
EXTENSION
OF
THE
RESULTS
TO
THE
CASE
OF
SYSTEM
(43.7)
WITH
ADDITIONAL
CONDITION
X
G
S
.
191
VIII
44.
FEJER
PROCESSES
FOR
REGULARIZED
LP
PROBLEMS
.
192
44.1.
THE
CASE
WHEN
THE
PROBLEM
L
IS
SOLVABLE
.
192
44.2.
THE
CASE
WHEN
THE
PROBLEM
L
IS
UNSOLVABLE
.
194
44.3.
DUAL
REGULARIZATION
OF
LP
PROBLEMS
.
195
CHAPTER
7.
PIECEWISE
LINEAR
FUNCTIONS
AND
PROBLEMS
OF
DISJUNCTIVE
PROGRAMMING
197
45.
INTRODUCTORY
CONSIDERATIONS
.
197
46.
A-EXTENSIONS
OF
LINEAR
FUNCTIONAL
SPACES
.
199
47.
THE
PROBLEM
ON
THE
SADDLE
POINT
OF
THE
DISJUNCTIVE
LAGRANGE
FUNCTION
.
203
48.
PIECEWISE
LINEAR
FUNCTIONS
AND
SYSTEMS
OF
PIECEWISE
LINEAR
INEQUALITIES
.
209
49.
THE
PROBLEM
OF
PIECEWISE
LINEAR
PROGRAMMING
.
212
49.1.
PRELIMINARY
REMARKS
.
212
49.2.
SOLVABILITY
CONDITIONS
FOR
THE
^-PROBLEM
.
213
49.3.
DUALITY
.
214
49.4.
SYMMETRIC
SETTING
OF
THE
PROBLEMS
(49.1)
AND
(49.6)
THAT
ARE
IN
THE
RELATION
OF
DUALITY
.
218
50.
DUALITY
FOR
IMPROPER
PROBLEMS
OF
PIECEWISE
LINEAR
PROGRAMMING
.
.
220
51.
THE
METHOD
OF
EXACT
PENALTY
FUNCTIONS
FOR
THE
PROBLEM
OF
PIECEWISE
LINEAR
PROGRAMMING
.
223
52.
QUESTIONS
OF
POLYHEDRAL
SEPARABILITY
.
225
APPENDIX.
ELEMENTS
OF
CONVEX
ANALYSIS
AND
CONVEX
PROGRAMMING
229
AL.
CONVEX
SETS
AND
CONVEX
FUNCTIONS
.
229
A2.
SUBDIFFERENTIABILITY
OF
CONVEX
FUNCTIONS
.
231
A3.
THE
PROBLEM
OF
CONVEX
PROGRAMMING
.
232
A4.
THE
THEOREM
ON
MARGINAL
VALUES
.
234
A5.
THE
PENALTY
FUNCTION
METHOD
FOR
PROBLEMS
OF
NONLINEAR
PROGRAMMING
.
236
A6.
AN
ESTIMATE
OF
DEVIATION
WITH
RESPECT
TO
THE
ARGUMENT
IN
THE
ASYMPTOTIC
PENALTY
METHOD
.
237
NOTATIONS
AND
ABBREVIATIONS
239
BIBLIOGRAPHY
241 |
| any_adam_object | 1 |
| author | Eremin, Ivan I. 1933- |
| author_GND | (DE-588)123234603 |
| author_facet | Eremin, Ivan I. 1933- |
| author_role | aut |
| author_sort | Eremin, Ivan I. 1933- |
| author_variant | i i e ii iie |
| building | Verbundindex |
| bvnumber | BV014189572 |
| callnumber-first | T - Technology |
| callnumber-label | T57 |
| callnumber-raw | T57.74.E74 2002 |
| callnumber-search | T57.74.E74 2002 |
| callnumber-sort | T 257.74 E74 42002 |
| callnumber-subject | T - General Technology |
| classification_rvk | QH 421 SK 870 |
| ctrlnum | (OCoLC)49229050 (DE-599)BVBBV014189572 |
| dewey-full | 519.7/2 519.7/221 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7/2 519.7/2 21 |
| dewey-search | 519.7/2 519.7/2 21 |
| dewey-sort | 3519.7 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV014189572 |
| illustrated | Illustrated |
| indexdate | 2024-08-23T00:36:08Z |
| institution | BVB |
| isbn | 906764353X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009726069 |
| oclc_num | 49229050 |
| open_access_boolean | |
| owner | DE-703 DE-824 DE-521 |
| owner_facet | DE-703 DE-824 DE-521 |
| physical | VIII, 248 S. graph. Darst. : 25 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | VSP |
| record_format | marc |
| series2 | Inverse and ill posed problems series |
| spelling | Eremin, Ivan I. 1933- Verfasser (DE-588)123234603 aut Theory of linear optimization I. I. Eremin 1. publ. Utrecht [u.a.] VSP 2002 VIII, 248 S. graph. Darst. : 25 cm txt rdacontent n rdamedia nc rdacarrier Inverse and ill posed problems series Literaturverz. S. 241 - 248 Linear programming Convex programming Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009726069&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Eremin, Ivan I. 1933- Theory of linear optimization Linear programming Convex programming Lineare Optimierung (DE-588)4035816-1 gnd |
| subject_GND | (DE-588)4035816-1 |
| title | Theory of linear optimization |
| title_auth | Theory of linear optimization |
| title_exact_search | Theory of linear optimization |
| title_full | Theory of linear optimization I. I. Eremin |
| title_fullStr | Theory of linear optimization I. I. Eremin |
| title_full_unstemmed | Theory of linear optimization I. I. Eremin |
| title_short | Theory of linear optimization |
| title_sort | theory of linear optimization |
| topic | Linear programming Convex programming Lineare Optimierung (DE-588)4035816-1 gnd |
| topic_facet | Linear programming Convex programming Lineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009726069&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ereminivani theoryoflinearoptimization |