Nonlinear and mixed integer optimization: fundamentals and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Oxford Univ. Press
1995
|
| Schriftenreihe: | Topics in chemical engineering
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 462 S. graph. Darst. |
| ISBN: | 0195100565 9780195100563 |
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| 264 | 1 | |a New York [u.a.] |b Oxford Univ. Press |c 1995 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: Nonlinear and mixed integer optimization
Autor: Floudas, Christodoulos A.
Jahr: 1995
Contents
1. Introduction, 3
1.1 Mathematical and Optimization Models, 3
1.2 Structure of Nonlinear and Mixed-Integer Optimization Models, 4
1.3 Illustrative Applications, 5
1.3.1 Binary Distillation Design, 6
1.3.2 Retrofit Design of Multiproduct Batch Plants, 8
1.3.3 Multicommodity Facility Location—Allocation, 11
1.4 Scope of the Book, 12
PART 1 FUNDAMENTALS OF CONVEX ANALYSIS AND
NONLINEAR OPTIMIZATION
2. Convex Analysis, 17
2.1 Convex Sets, 17
2.1.1 Basic Definitions, 17
2.1.2 Convex Combination and Convex Hull, 20
2.1.3 Separation of Convex Sets, 22
2.1.4 Support of Convex Sets, 24
2.2 Convex and Concave Functions, 24
2.2.1 Basic Definitions, 25
2.2.2 Properties of Convex and Concave Functions, 25
2.2.3 Continuity and Semicontinuity, 27
2.2.4 Directional Derivative and Subgradients, 30
2.2.5 Differentiable Convex and Concave Functions, 31
2.2.6 Minimum (Infimum) and Maximum (Supremum), 34
2.2.7 Feasible Solution, Local and Global Minimum, 36
2.3 Generalizations of Convex and Concave Functions, 37
2.3.1 Quasi-convex and Quasi-concave Functions, 37
2.3.2 Properties of Quasi-convex and Quasi-concave Functions, 39
2.3.3 Differentiable Quasi-convex, Quasi-concave Functions, 40
2.3.4 Pseudo-convex and Pseudo-concave Functions, 40
2.3.5 Properties of Pseudo-convex and Pseudo-concave Functions, 40
2.3.6 Relationships among Convex, Quasi-convex and Pseudo-convex Functions, 41
.H!
3. Fundamentals of Nonlinear Optimization, 45
3.1 Unconstrained Nonlinear Optimization, 45
3.1.1 Formulation and Definitions, 45
3.1.2 Necessary Optimally Conditions, 46
3.1.3 Sufficient Optimality Conditions, 47
3.1.4 Necessary and Sufficient Optimality Conditions, 48
3.2 Constrained Nonlinear Optimization, 49
3.2.1 Formulation and Definitions, 49
3.2.2 Lagrange Functions and Multipliers, S1
3.2.3 Interpretation of Lagrange Multipliers, 52
3.2.4 Existence of Lagrange Multipliers, 54
3.2.5 Weak Lagrange Functions, 56
3.2.6 First-Order Necessary Optimality Conditions, 56
3.2.7 First-Order Sufficient Optimality Conditions, 61
3.2.8 Saddle Point and Optimality Conditions, 62
3.2.9 Second-Order Necessary Optimality Conditions, 64
3.2.10 Second-Order Sufficient Optimality Conditions, 67
3.2.11 Outline of Nonlinear Algorithmic Methods, 68
4. Duality Theory, 75
4.1 Primal Problem, 75
4.1.1 Formulation, 75
4.1.2 Perturbation Function and Its Properties, 76
4.1.3 Stability of Primal Problem, 76
4.1.4 Existence of Optimal Multipliers, 77
4.2 Dual Problem, 77
4.2.1 Formulation, 78
4.2.2 Dual Function and Its Properties, 78
4.2.3 Illustration of Primal-Dual Problems, 79
4.2.4 Geometrical Interpretation of Dual Problem, 80
4.3 Weak and Strong Duality, 82
4.3.1 Illustration of Strong Duality, 84
4.3.2 Illustration of Weak and Strong Duality, 85
4.3.3 Illustration of Weak Duality, 86
4.4 Duality Gap and Continuity of Perturbation Function, 87
4.4.1 Illustration of Duality Gap, 88
PART 2 FUNDAMENTALS OF MIXED-INTEGER OPTIMIZATION
5. Mixed-Integer Linear Optimization, 95
5.1 Motivation, 95
5.2 Formulation, 96
5.2.1 Mathematical Description, 96
5.2.2 Complexity issues in MILP, 96
5.2.3 Outline of MILP Algorithms, 97
5.3 Branch and Bound Method, 98
5.3.1 Basic Notions, 98
Contents xiii
5.3.2 General Branch and Bound Framework, 101
5.3.3 Branch and Bound Based on Linear Programming Relaxation, 103
6. Mixed-Integer Nonlinear Optimization, 109
6.1 Motivation, 109
6.2 Formulation, 110
6.2.1 Mathematical Description, 111
6.2.2 Challenges/Difficulties in MINLP, 112
6.2.3 Overview of MINLP Algorithms, 112
6.3 Generalized Benders Decomposition, GBD, 114
6.3.1 Formulation, 114
6.3.2 Basic Idea, 115
6.3.3 Theoretical Development, 116
6.3.4 Algorithmic Development, 112
6.3.5 Variants of GBD, 125
6.3.6 GBD in Continuous and Discrete-Continuous Optimization, 140
6.4 Outer Approximations, OA, 144
6.4.1 Formulation, 144
6.4.2 Basic Idea, 145
6.4.3 Theoretical Development, 145
6.4.4 Algorithmic Development, 151
6.5 Outer Approximation with Equality Relaxation, OA/ER, 155
6.5.1 Formulation, 155
6.5.2 Basic Idea, 156
6.5.3 Theoretical Development, 156
6.5.4 Algorithmic Development, 160
6.5.5 Illustration, 161
6.6 Outer Approximation with Equality Relaxation and Augmented Penalty, OA/ER/AP, 168
6.6.1 Formulation, 168
6.6.2 Basic Idea, 169
6.6.3 Theoretical Development, 169
6.6.4 Algorithm Development, 170
6.6.5 Illustration, 171
6.7 Generalized Outer Approximation, GOA, 175
6.7.1 Formulation, 175
6.7.2 Basic Idea, 175
6.7.3 Theoretical Development, 176
6.7.4 Algorithmic Development, 179
6.7.5 Worst-Case Analysis of GOA, 180
6.7.6 Generalized Outer Approximation with Exact Penalty, GOA/EP, 181
6.8 Comparison of GBD and OA-based Algorithms, 183
6.8.1 Formulation, 183
6.8.2 Nonlinear Equality Constraints, 184
6.8.3 Nonlinearities in y and Joint x-y, 184
6.8.4 The Primal Problem, 186
6.8.5 The Master Problem, 187
6.8.6 Lower Bounds, 189
6.9 Generalized Cross Decomposition, GCD, 190
6.9.1 Formulation, 190
6.9.2 Basic Idea 191
6.9.3 Theoretical Development, 191
6.9.4 Algorithmic Development, 199
6.9.5 GCD under Separability, 203
6.9.6 GCD In Continuous and Discrete-Continuous Optimization, 208
PART 3 APPLICATIONS IN PROCESS SYNTHESIS
7. Process Synthesis, 225
7.1 Introduction, 225
7.1.1 The Overall Process System, 226
7.2 Definition, 229
7.2.1 Difficulties/Challenges in Process Synthesis, 230
7.3 Approaches in Process Synthesis, 232
7.4 Optimization Approach in Process Synthesis, 233
7.4.1 Outline, 233
7.4.2 Representation of Alternatives, 234
7.4.3 Mathematical Model of Superstructure, 235
7.4.4 Algorithmic Development, 256
7.5 Application Areas, 257
8. Heat Exchanger Network Synthesis, 259
8.1 Introduction, 259
8.2 Problem Statement, 261
8.2.1 Definition of Temperature Approaches, 262
8.3 Targets for HEN Synthesis, 262
8.3.1 Minimum Utility Cost, 262
8.3.2 Minimum Number of Matches, 280
8.3.3 Minimum Number of Matches for Vertical Heat Transfer, 294
8.4. Decomposition-based HEN Synthesis Approaches, 304
8.4.1 Heat Exchanger Network Derivation, 305
8.4.2 HEN Synthesis Strategy, 321
8.5 Simultaneous HEN Synthesis Approaches, 323
8.5.1 Simultaneous Matches-Network Optimization, 324
8.5.2 Pseudo-Pinch, 338
8.5.3 Synthesis of HENs Without Decomposition, 342
8.5.4 Simultaneous Optimization Models for HEN Synthesis, 356
9. Distillation-based Separation Systems Synthesis, 379
9.1 Introduction, 379
9.2 Synthesis of Heat-integrated Sharp Distillation Sequences, 381
9.2.1 Problem Statement 382
9.2.2 Basic Idea, 382
9.2.3 Derivation of Superstructure, 383
9.2.4 Mathematical Formulation of Superstructure, 385
Contents
9.3 Synthesis of Nonsharp Distillation Sequences, 393
9.3.1 Problem Statement, 396
9.3.2 Basic Idea, 396
9.3.3 Nonsharp Separation Superstructure, 397
9.3.4 Mathematical Formulation of Nonsharp Separation Superstructure, 400
10. Synthesis of Reactor Networks and Reactor-Separator-Recycle Systems, 407
10.1 Introduction, 407
10.2 Synthesis of Isothermal Reactor Networks, 411
10.2.1 Problem Statement, 411
10.2.2 Basic Idea, 412
10.2.3 Reactor Unit Representation, 412
10.2.4 Reactor Network Superstructure, 414
10.2.5 Mathematical Formulation of Reactor Superstructure, 415
10.3 Synthesis of Reactor-Separator-Recycle Systems, 422
10.3.1 Introduction, 422
10.3.2 Problem Statement, 424
10.3.3 Basic Idea, 424
10.3.4 Reactor-Separator-Recycle Superstructure, 425
10.3.5 Mathematical Formulation, 428
Bibliography, 435
Index, 453
|
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| spelling | Floudas, Christodoulos A. 1959- Verfasser (DE-588)13590854X aut Nonlinear and mixed integer optimization fundamentals and applications Christodoulos A. Floudas New York [u.a.] Oxford Univ. Press 1995 XV, 462 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Topics in chemical engineering Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 s DE-604 Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007409833&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Floudas, Christodoulos A. 1959- Nonlinear and mixed integer optimization fundamentals and applications Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| subject_GND | (DE-588)4156566-6 (DE-588)4128192-5 |
| title | Nonlinear and mixed integer optimization fundamentals and applications |
| title_auth | Nonlinear and mixed integer optimization fundamentals and applications |
| title_exact_search | Nonlinear and mixed integer optimization fundamentals and applications |
| title_full | Nonlinear and mixed integer optimization fundamentals and applications Christodoulos A. Floudas |
| title_fullStr | Nonlinear and mixed integer optimization fundamentals and applications Christodoulos A. Floudas |
| title_full_unstemmed | Nonlinear and mixed integer optimization fundamentals and applications Christodoulos A. Floudas |
| title_short | Nonlinear and mixed integer optimization |
| title_sort | nonlinear and mixed integer optimization fundamentals and applications |
| title_sub | fundamentals and applications |
| topic | Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Gemischt-ganzzahlige Optimierung Nichtlineare Optimierung |
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