Cover
Half-title
Series information
Title page
Copyright information
Dedication
Contents
Preface
1 Optimization in Process Systems Engineering
1.1 Introduction
1.2 Classification of Optimization Models
1.3 Outline of the Book
2 Solving Nonlinear Equations
2.1 Process Modeling Approaches
2.2 Newton's Method
2.3 Quasi-Newton Methods
Exercises
3 Basic Theoretical Concepts in Optimization
3.1 Basic Formulations
3.2 Nonlinear Programming Example
3.3 Basic Concepts
3.4 Optimality Conditions
3.4.1 Unconstrained Optimization
3.4.2 Constrained Optimization (Equalities)
3.4.3 Constrained Optimization (Inequalities)
3.4.4 Nonlinear Programming Problem
3.4.5 Active-Set Strategy Procedure for Determining a Karush-Kuhn-Tucker Point (Sargent, 1975)
Exercises
4 Nonlinear Programming Algorithms
4.1 Successive-Quadratic Programming
4.2 Reduced-Gradient Method
4.3 Interior-Point Method
4.4 Comparison of NLP Algorithms
4.5 Guidelines for Formulating NLP Models
Exercises
5 Linear Programming
5.1 Basic Theory
5.2 Simplex Algorithm
5.3 Numerical Example
Exercises
6 Mixed-Integer Programming Models
6.1 Modeling with 0-1 Variables
6.1.1 Motivating Examples
6.1.2 Modeling with Linear 0-1 Variables yj
6.1.3 Some Common IP Problems
6.1.3.1 Assignment Problem
6.1.3.2 Plant Location Problem
6.1.3.3 Knapsack Problem
6.1.3.4 Set-Covering Problem
6.1.3.5 Traveling Salesman Problem
Exercises
7 Systematic Modeling of Constraints with Logic
7.1 Modeling 0-1 Constraints with Propositional Logic
7.1.1 Example 1 of Logic Proposition
7.1.2 Example 2 of Logic Proposition
7.2 Modeling of Disjunctions
7.2.1 Big-M Reformulation
7.2.2 Convex-Hull Reformulation
7.2.3 Example
7.3 Generalized Disjunctive Programming
Exercises
8 Mixed-Integer Linear Programming
8.1 Introduction
8.2 MILP Methods
8.3 Gomory Cutting Planes
8.4 Branch and Cut Method
Exercises
9 Mixed-Integer Nonlinear Programming
9.1 Overview of Solution Methods
9.2 Derivation of Outer-Approximation and Generalized Benders Decomposition Methods
9.3 Extended Cutting-Plane Method
9.4 Properties and Extensions
Exercises
10 Generalized Disjunctive Programming
10.1 Logic-Based Formulation for Discrete/Continuous Optimization
10.2 Relaxations and Reformulations of GDP
10.3 Special Purpose Methods for GDP
10.3.1 Disjunctive Branch and Bound
10.3.2 Logic-Based Outer Approximation
Exercises
11 Constraint Programming
11.1 Logic-Based Modeling
11.2 Search in Constraint Programming
11.2.1 Domain Reduction and Constraint Propagation
11.2.2 Tree Search
Exercises
12 Nonconvex Optimization
12.1 Major Approaches to Global Optimization
12.2 Convexification
12.3 Global Optimization of Bilinear Programs
12.4 Global Optimization of More General Functions
Exercises
13 Lagrangean Decomposition
13.1 Overview of Decomposition for Large-Scale Problems
13.2 Lagrangean Relaxation
13.3 Lagrangean Dual
13.4 Lagrangean Decomposition
13.5 Update of Lagrange Multipliers
Exercises
14 Stochastic Programming
14.1 Strategies for Optimization under Uncertainty
14.2 Linear Stochastic Programming
14.3 L-Shaped Method
14.4 Multistage Stochastic Programming
14.5 Robust Optimization
Exercises
15 Flexibility Analysis
15.1 Introduction
15.2 Two-Stage Programming with Guaranteed Feasibility
15.3 Flexibility Analysis
15.4 Flexibility Test with No Control Variables
15.5 Flexibility Test with Control Variables
15.6 Parametric Region of Feasible Operation and Vertex Search
15.7 Flexibility Index and Vertex Search
15.8 Theoretical Conditions for Vertex Solutions
15.9 Active-Set Strategy
Exercises
Appendix A Modeling Systems and Optimization Software
A.1 Modeling Systems
A.2 Optimization Software: LP, MILP, NLP, MINLP, GDP
A.2.1 Optimization Software Reviews
A.2.2 Solvers and Corresponding Links
LP
MILP
MIQP
NLP
MINLP
GDP
NEOS Server
A.2.3 References on Optimization Software
A.2.4 Libraries Test Problems
Mittleman Collection of NLP Problems
CUTE Test Problems
MINLPLib: A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
MINLP (instances minlp.org)
CMU-IBM Open Source MINLP Project
SIPLIB: A Stochastic Integer Programming Test Problem Library
Appendix B Optimization Models for Process Systems Engineering
B.1 Web-Based Software for Mixed-Integer Programming Applications in Process Systems Engineering
BatchMPC
BatchSPC
CENTRALIZED/DECENTRALIZED
CHP
CRUDEOIL
CRUDEOIL DISCRETE: (MILP)
CRUDEOIL CONTINUOUS: (MINLP)
CYCLE
DECAY
DISIM
EXTRACTOR
FLEXNET
GDP-DISTILL
GREENPLAN
LOGMIP
MINLP Cyberinfrastructure
MULTIPERIOD BLEND
MULTISTAGE
NETCHAIN
OILGASPLAN
PowerSCHEDULE
PRODEV
REL OPT
Resilient Supply Chain
SIMPLAN
SIMPRONET
STEAM
STN
For discrete-time model
For continuous-time model
SYNHEAT
THERMAL-DIST
WATER
WATERNET
WATERTREAT
B.2 CMU-IBM Cyber-Infrastructure for MINLP Collaborative Site
MINLP Library
GDP Library
References
Index