Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming

Theory, Algorithms, Software, and Applications

By: Mohit Tawarmalani, Nikolaos Sahinidis

Write A Review

Hardcover | 31 October 2002

At a Glance

Hardcover
508 Pages

Dimensions(cm)
23.39 x 15.6 x 2.87

Hardcover

$349.17

or 4 interest-free payments of $87.29 with

or

Aims to ship in 7 to 10 business days

Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Production & Industrial Engineering

Introduction to Operations Research

11th Edition

Paperback

RRP $159.95

$130.75

18%
OFF

Particle-fluid and Multiphase Flows : Particle-fluid and Multiphase Flows - Aibing Yu

$146.80

41%
OFF

Process Improvement Essentials

O'Reilly Ser.

Paperback

RRP $85.50

$39.75

54%
OFF

Introduction to Manufacturing

An Industrial Engineering and Management Perspective

Paperback

RRP $131.00

$105.50

19%
OFF

Troubleshooting and Root Cause Failure Analysis

Equipment Problem Solving

Paperback

RRP $84.99

$71.25

16%
OFF

In-Home Medication : Integrating Multidisciplinary Perspectives in Design-Driven Pharma Practices - Antonella Valeria Penati

$44.25

32%
OFF

Circular Economy: The Next Level of Company Success : A Comprehensive Study on How to Create Value and Improve Operational Excellence Through Circularity - Andre Podleisek

Proceedings of the 4th International Conference on Intelligence-Based Transformations of Technology and Business Trends (ICITTBT-2024)

Hardcover

$534.50

Machine Learning and Artificial Intelligence in Healthcare Systems : Tools and Techniques - Tawseef Ayoub Shaikh

$124.75

40%
OFF

Preface	p. xiii
Acknowledgments	p. xvii
List of Figures	p. xix
List of Tables	p. xxiii
Introduction	p. 1
The Mixed-Integer Nonlinear Program	p. 5
Branch-and-Bound	p. 6
Illustrative Example	p. 8
A Separable Relaxation	p. 9
Tighter Relaxation	p. 12
Optimality-Based Range Reduction	p. 12
Drawing Inferences from Constraints	p. 16
Branching on the Incumbent	p. 17
Outline of this Book	p. 18
Convex Extensions	p. 25
Introduction	p. 26
Convex Extensions of l.s.c. Functions	p. 29
Multilinear Functions	p. 40
Analysis of Convex Underestimators of x/y	p. 43
Convex Envelope of x/y	p. 44
Closed-Form Expression of Convex Envelope	p. 45
Theoretical Comparison of Underestimators	p. 47
Numerical Example	p. 52
Concave Envelope of x/y	p. 56
Relaxing the Positivity Requirement	p. 57
Semidefinite Relaxation of x/y	p. 60
Generalizations and Applications	p. 62
Envelopes of (ax + by)/(cx + dy)	p. 64
Convex Envelope of f(x)y[superscript 2]	p. 65
Convex Envelope of f(x)/y	p. 69
Summation of Functions	p. 69
Product Disaggregation	p. 71
Introduction	p. 72
Preliminaries	p. 75
Reformulations of a Rational Function	p. 77
Tightness of the Reformulation Scheme	p. 81
Special Instances of the Reformulation	p. 91
Examples of the Reformulation Scheme	p. 93
Example 1: Hock & Schittkowski (1981)	p. 94
Example 2: Nuclear Reactor Reload Pattern Design	p. 95
Example 3: Catalyst Mixing for Packed Bed Reactor	p. 97
Reformulations of Hyperbolic Programs	p. 100
Upper Bounding of 0-1 Hyperbolic Programs	p. 105
A Branch-and-Bound Algorithm	p. 108
Cardinality Constrained Hyperbolic Programs	p. 110
Computational Results for CCH Programs	p. 111
Comparison of Bounds	p. 112
Performance of the Proposed Algorithm	p. 112
p-Choice Facility Location	p. 115
Relaxations of Factorable Programs	p. 125
Nonlinear Relaxation Construction	p. 125
Concavoconvex Functions	p. 130
Polyhedral Outer-Approximation	p. 132
Domain Reduction	p. 147
Preliminaries	p. 147
Legendre-Fenchel Transform	p. 148
Lagrangian Relaxation	p. 152
An Iterative Algorithm for Domain Reduction	p. 153
Theoretical Framework: Abstract Minimization	p. 154
Application to Traditional Models	p. 160
Geometric Intuition	p. 163
Domain Reduction Problem: Motivation	p. 163
Relation to Earlier Works	p. 164
Bounds Via Monotone Complementarity	p. 177
Tightening using Reduced Costs	p. 178
Linearity-based Tightening	p. 179
Probing	p. 181
Learning Reduction Procedure	p. 183
Node Partitioning	p. 189
Introduction	p. 189
Partitioning Factorable Programs	p. 190
Branching Variable Selection	p. 190
Branching Point Selection	p. 194
Finiteness Issues	p. 196
Stochastic Integer Programs	p. 197
The Question of Finiteness	p. 198
Key to Finiteness	p. 199
Lower Bounding Problem	p. 200
Upper Bounding	p. 202
Branching Scheme	p. 203
Finiteness Proof	p. 205
Enhancements	p. 205
Extension to Mixed-Integer Recourse	p. 207
Computational Results for Stochastic Programs	p. 207
Implementation	p. 213
Design Philosophy	p. 213
Programming Languages and Portability	p. 215
Supported Optimization Solvers	p. 216
Data Storage and Associated Algorithms	p. 216
Management of Work-Array	p. 216
List of Open Nodes	p. 217
Module Storage: Factorable Programming	p. 218
Evaluating Derivatives	p. 219
Algorithmic Enhancements	p. 221
Multiple Solutions	p. 221
Local Upper Bounds	p. 222
Postponement	p. 222
Finite Branching Schemes	p. 223
Debugging Facilities	p. 224
BARON Interface	p. 224
Refrigerant Design Problem	p. 229
Introduction	p. 229
Problem Statement	p. 230
Previous Work	p. 231
Optimization Formulation	p. 232
Modeling Physical Properties	p. 235
Modeling Structural Constraints	p. 239
Multiple Solutions	p. 249
Computational Results	p. 249
The Pooling Problem	p. 253
Introduction	p. 254
The p- and q-Formulations	p. 256
The p-Formulation	p. 256
The q-Formulation	p. 261
The pq-Formulation	p. 264
Properties of the pq-Formulation	p. 266
Lagrangian Relaxations	p. 273
Global Optimization of the Pooling Problem	p. 276
Branching Strategy	p. 278
Computational Experience	p. 279
Miscellaneous Problems	p. 285
Separable Concave Quadratic Programs	p. 285
Indefinite Quadratic Programs	p. 289
Linear Multiplicative Programs	p. 293
Generalized Linear Multiplicative Programs	p. 297
Univariate Polynomial Programs	p. 298
Miscellaneous Benchmark Problems	p. 298
Selected Mixed-Integer Nonlinear Programs	p. 305
Design of Just-in-Time Flowshops	p. 305
The Gupta-Ravindran Benchmarks	p. 311
GAMS/BARON: A Tutorial	p. 313
Introduction	p. 314
Types of Problems GAMS/BARON Can Solve	p. 315
Factorable Nonlinear Programming: MIP, NLP, and MINLP	p. 315
Special Cases of BARON's Factorable Nonlinear Programming Solver	p. 316
Software and Hardware Requirements	p. 320
Model Requirements	p. 320
Variable and Expression Bounds	p. 320
Allowable Nonlinear Functions	p. 321
How to Run GAMS/BARON	p. 321
System Output	p. 322
System Log	p. 322
Termination Messages, Model and Solver Status	p. 324
Algorithmic and System Options	p. 325
Application to Multiplicative Programs	p. 325
LMPs of Type 1	p. 326
Controlling Local Search Requirements	p. 329
Reducing Memory Requirements via Branching Options	p. 331
Controlling Memory Requirements via Probing	p. 333
Effects of Reformulation	p. 334
LMPs of Type 2	p. 335
Controlling Time Spent on Preprocessing LPs	p. 339
LMPs of Type 3	p. 342
Comparison with Local Search	p. 347
Application to Pooling Problems	p. 356
Controlling Time Spent in Preprocessing	p. 364
Reducing Memory Requirements	p. 368
Controlling the Size of the Search Tree	p. 368
Controlling Local Search Time During Navigation	p. 371
Reduced Branching Space	p. 371
Pooling Problem Computations	p. 372
Problems from globallib and minlplib	p. 376
Local Landscape Analyzer	p. 380
Finding the K Best or All Feasible Solutions	p. 383
Motivation and Alternative Approaches	p. 383
Finding All Solutions to Combinatorial Optimization Problems	p. 385
Refrigerant Design Problem	p. 391
Finding All Solutions to Systems of Nonlinear Equations	p. 394
GAMS Models for Pooling Problems	p. 403
Problems Adhya 1, 2, 3, and 4	p. 403
Problems Bental 4 and 5	p. 411
Problems Foulds 2, 3, 4, and 5	p. 416
Problems Haverly 1, 2, and 3	p. 428
Problem RT 2	p. 431
Bibliography	p. 435
Index	p. 463
Author Index	p. 469
Table of Contents provided by Ingram. All Rights Reserved.

Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming

Theory, Algorithms, Software, and Applications

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

More in Production & Industrial Engineering

Introduction to Operations Research

11th Edition

Particle-fluid and Multiphase Flows

Particle-fluid and Multiphase Flows

Reliability Analysis of Modern Power Systems

Process Improvement Essentials

O'Reilly Ser.

Introduction to Manufacturing

An Industrial Engineering and Management Perspective

Troubleshooting and Root Cause Failure Analysis

Equipment Problem Solving

In-Home Medication

Integrating Multidisciplinary Perspectives in Design-Driven Pharma Practices

Innovations in Healthcare Technologies in India

An Initiative of Icmr-Cibiod (Centre for Innovation and Bio-Design)

Introduction to Mechanical Engineering

Part 2

Curtiss Aerocar

1928-1940

Circular Economy: The Next Level of Company Success

A Comprehensive Study on How to Create Value and Improve Operational Excellence Through Circularity

Advances in Design and Automation

Select Proceedings of Icfammt 2024

Role of Artificial Intelligence, Telehealth, and Telemedicine in Medical Virology

Medical Virology: From Pathogenesis to Disease Control

Laser Additive Remanufacturing and Life Extension Technology

Additive Manufacturing Technology

Advances in Mechanical Engineering

Select Proceedings of Icrame 2023

International Conference on Systems and Technologies for Smart Agriculture

Springer Proceedings in Information and Communication Technologies

Petroleum Refining and Technology

Recent Trends in Mechanical Engineering

Select Proceedings of Icrame 2024

Bridging Horizons in Artificial Intelligence, Robotics, Cybersecurity, Smart Cities, and Digital Economy

Proceedings of the 4th International Conference on Intelligence-Based Transformations of Technology and Business Trends (ICITTBT-2024)

Machine Learning and Artificial Intelligence in Healthcare Systems

Tools and Techniques

Handbook of Decision Analysis

Wiley Series in Operations Research and Management Science

Emerging Trends in Traditional and Technical Textiles

Select Proceedings of Icett 2023

Advanced Manufacturing Processes

Integration of Sustainable Approaches

Recent Advances in Additive Manufacturing

Select Proceedings of Icam 2024

This product is categorised by

Popular Searches