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El. knyga: Optimization for Chemical and Biochemical Engineering: Theory, Algorithms, Modeling and Applications

, (University of Cambridge), (Imperial College London),
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Discover the subject of optimization in a new light with this modern and unique treatment. Includes a thorough exposition of applications and algorithms in sufficient detail for practical use, while providing you with all the necessary background in a self-contained manner. Features a deeper consideration of optimal control, global optimization, optimization under uncertainty, multiobjective optimization, mixed-integer programming and model predictive control. Presents a complete coverage of formulations and instances in modelling where optimization can be applied for quantitative decision-making. As a thorough grounding to the subject, covering everything from basic to advanced concepts and addressing real-life problems faced by modern industry, this is a perfect tool for advanced undergraduate and graduate courses in chemical and biochemical engineering.

Recenzijos

'This book offers a very clear, uncluttered presentation of key ideas of optimisation in rigorous form and with plenty of examples from a decade of research and educational experience. It offers an exceptional resource for educators and students of optimisation methods, as well as a valuable reference text to practitioners.' Alexei Lapkin, University of Cambridge 'This excellent book brings together important and up-to-date elements of the theory and practice of optimisation with application to chemical and biochemical engineering. It's an ideal reference for students on advanced courses or for researchers in the field.' Nilay Shah, Imperial College

Daugiau informacijos

Modern and unique treatment of process optimization which presents an exposition of applications and algorithms in detail for practical use.
Notation xii
Preface xiii
PART I OVERVIEW OF OPTIMIZATION: APPLICATIONS AND PROBLEM FORMULATIONS
1(28)
1 Introduction To Optimization
3(26)
1.1 Statement Of General Mathematical Programming (Mp) (Optimization) Problem
3(3)
1.2 Applications In Technological And Scientific Problems
6(8)
1.3 Algorithms and Complexity
14(6)
1.4 Generalized Optimization Problems
20(5)
1.5
Chapter Summary
25(1)
1.6 References
25(1)
1.7 Further Reading Recommendations
26(3)
PART II FROM GENERAL MATHEMATICAL BACKGROUND TO GENERAL NONLINEAR PROGRAMMING PROBLEMS (NLP)
29(84)
2 General Concepts
31(7)
2.1 "Size of Vectors"
31(1)
2.2 Minimization versus Maximization
32(1)
2.3 Types of Extrema of a Function (Stationary Points)
32(1)
2.4 Contours of f(x)
33(1)
2.5 Vectors, and Derivatives Involving Matrices and Vectors
34(3)
2.6 Further Reading Recommendations
37(1)
3 Convexity
38(6)
3.1 Definition of Convex Function
38(3)
3.2 Convex Sets
41(1)
3.3 Further Reading Recommendations
42(1)
3.4 Exercises
42(2)
4 Quadratic Functions
44(13)
4.1 Construction of the Matrix Form of a Quadratic Function by Example
44(1)
4.2 Eigenvalues of Q for Quadratic Functions and Convexity
45(4)
4.3 Geometrical Interpretation of Eigenvalues and Eigenvectors
49(1)
4.4 Solution of an Unconstrained Quadratic Program (QP)
50(1)
4.5 Least Squares Fitting and Its Relation to QP
51(5)
4.6 Further Reading Recommendations
56(1)
4.7 Exercises
56(1)
5 Minimization In One Dimension
57(6)
5.1 Bisection
57(1)
5.2 Golden Section Search
57(3)
5.3 Newton's Method
60(1)
5.4 Other Methods
61(1)
5.5 Further Reading Recommendations
61(1)
5.6 Exercises
62(1)
6 Unconstrained Multivariate Gradient-Based Minimization
63(18)
6.1 Minimum Stationary Points
63(1)
6.2 Calculating Derivatives
64(2)
6.3 The Steepest Descent Method
66(1)
6.4 Newton's Method
67(2)
6.5 Rate of Convergence
69(3)
6.6 The Newton Family of Methods
72(1)
6.7 Optimization Termination Criteria
73(1)
6.8 Linesearch Methods
74(3)
6.9 Summary of the
Chapter
77(1)
6.10 References
77(1)
6.11 Exercises
77(4)
7 Constrained Nonlinear Programming Problems (Nlp)
81(10)
7.1 Convexity of Constraint Set
81(1)
7.2 Convex Programming Problem
81(1)
7.3 Lagrange Multipliers
82(3)
7.4 Necessary Conditions of Optimality (KKT Conditions)
85(1)
7.5 Sufficient Conditions
85(2)
7.6 Discussion and Solution Procedures
87(1)
7.7 References
88(1)
7.8 Further Reading Recommendations
88(1)
7.9 Exercises
89(2)
8 Penalty And Barrier Function Methods
91(10)
8.1 Penalty Functions
91(3)
8.2 Barrier Methods: Logarithmic Barriers
94(2)
8.3 Penalty-Multiplier Method (Augmented Lagrangian Method)
96(3)
8.4 Further Reading Recommendations
99(1)
8.5 Exercises
99(2)
9 Interior Point Methods (Ipm's): A Detailed Analysis
101(12)
9.1 NLP Formulations and Lagrangians
101(1)
9.2 Logarithmic Barrier Functions for Inequality Constrained NLPs
102(3)
9.3 Reformulating NLP Problems into Canonical Form
105(1)
9.4 Newton's Method for NLP with Equality Constraints Only
106(1)
9.5 Logarithmic Barriers for NLPs with Equalities and Bounds
107(4)
9.6 Summary of Interior Point Methods
111(1)
9.7 References
112(1)
9.8 Further Reading Recommendations
112(1)
PART III FORMULATION AND SOLUTION OF LINEAR PROGRAMMING (LP) PROBLEMS
113(223)
10 Introduction To Lp Models
115(8)
10.1 General LP Problem Model
115(1)
10.2 Geometrical Solution and Interpretation of LP Problems
116(6)
10.3 Further Reading Recommendations
122(1)
11 Numerical Solution Of Lp Problems Using The Simplex Method
123(10)
11.1 Introduction
123(1)
11.2 Rectangular Systems of Linear Equations
123(2)
11.3 Rectangular Systems and the Objective Function of the LP Problem
125(1)
11.4 The Simplex Method
126(2)
11.5 Revisiting the Use of Artificial Variables for an Initial Basic Solution
128(1)
11.6 Numerical Examples of the Simplex Method
128(2)
11.7 References
130(1)
11.8 Further Reading Recommendations
130(1)
11.9 Exercises
131(2)
12 A Sampler Of Lp Problem Formulations
133(13)
12.1 Product Mix Problem
133(1)
12.2 Diet Problem
134(1)
12.3 Blending Problem
135(1)
12.4 Transportation Problem
136(2)
12.5 Linear ODE Optimal Control Problem (OCP)
138(5)
12.6 Further Reading Recommendations
143(1)
12.7 Exercises
144(2)
13 Regression Revisited: Using Lp To Fit Linear Models
146(5)
13.1 l2 / Euclidean Norm Fitting (Least Squares)
146(1)
13.2 l1 Norm Fitting
147(1)
13.3 l∞ Norm Fitting
148(1)
13.4 Application: Antoine Vapor Pressure Correlation Fitting
148(2)
13.5 Further Reading Recommendations
150(1)
14 Network Flow Problems
151(10)
14.1 Network, Arcs, Graphs
151(1)
14.2 Minimum Cost Network Flow Problem
152(1)
14.3 Integrality of Solution Theorem
153(1)
14.4 Capacitated Minimum Cost Network Flow Problem
154(1)
14.5 Shortest Path (or Minimum Distance) Problem
154(1)
14.6 Transportation Problem
155(2)
14.7 Transshipment Problem
157(1)
14.8 The Assignment Problem
158(1)
14.9 References
159(1)
14.10 Further Reading Recommendations
159(1)
14.11 Exercises
159(2)
15 Lp And Sensitivity Analysis, In Brief
161(7)
15.1 The Value of Lagrange Multipliers
161(1)
15.2 Lagrange Multipliers in LP
161(2)
15.3 Example of Sensitivity Analysis
163(3)
15.4 Summary of
Chapter
166(1)
15.5 Further Reading Recommendations
167(1)
16 Multiobjective Optimization
168(27)
16.1 Problem Statement
168(2)
16.2 Pareto Optimality Theory
170(3)
16.3 Solution Procedures Generating Pareto Points
173(12)
16.4 Pareto Solution Sets
185(4)
16.5 Conclusions and further reading
189(1)
16.6 Problems
190(1)
16.7 References
191(2)
16.8 Further Reading
193(2)
17 Optimization Under Uncertainty
195(33)
17.1 Introduction
195(2)
17.2 Different Approaches to Address Optimization Under Uncertainty
197(6)
17.3 Robust Optimization
203(2)
17.4 Sample Average Approximation Method
205(3)
17.5 Scenario Generation and Sampling Methods
208(4)
17.6 Sampling Methods for Scenario Generation
212(6)
17.7 Solutions on Average Approximation Algorithm
218(1)
17.8 Flexibility Analysis of Chemical Processes
218(6)
17.9 References
224(1)
17.10 Further Reading Recommendations
225(1)
17.11 Exercises
226(2)
18 Mixed-Integer Programming Problems
228(33)
18.1 Preliminaries to Solving Mixed-Integer Programming Problems
229(4)
18.2 Solution Techniques for Mixed-Integer Linear Programming Problems (MILP)
233(11)
18.3 Solution Techniques for MINLP Problems
244(14)
18.4 References
258(1)
18.5 Further Reading Recommendations
259(1)
18.6 Exercises
260(1)
19 Global Optimization
261(26)
19.1 Introduction
261(1)
19.2 Problem Statement
262(5)
19.3 Reducing the Domain for a Branch and Reduce Approach
267(6)
19.4 Underestimators
273(7)
19.5 Tunneling
280(2)
19.6 Pseudocode for a Global Optimization Algorithm
282(1)
19.7 References
283(1)
19.8 Further Reading Recommendations
284(1)
19.9 Exercises
285(2)
20 Optimal Control Problems (Dynamic Optimization)
287(25)
20.1 Problem Statement, Single-Stage and Multistage Problems
287(5)
20.2 Pontryagin's Minimum (Maximum) to Solve Single-Stage Dynamics
292(4)
20.3 Transcription to NLP Problems via Discretization
296(8)
20.4 Control and State Parameterization via Orthogonal Collocation
304(6)
20.5 References
310(1)
20.6 Further Reading Recommendations
311(1)
20.7 Exercises
311(1)
21 System Identification And Model Predictive Control
312(24)
21.1 Introduction
312(1)
21.2 Dynamical Systems
313(6)
21.3 Introduction to System Identification
319(7)
21.4 Introduction to Model Predictive Control (MPC)
326(6)
21.5 Discussion on the Impact of Optimization Algorithms on Identification and MPC
332(1)
21.6 References
332(2)
21.7 Exercises
334(2)
Index 336
Vassilios S. Vassiliadis is a Senior Lecturer in the Department of Chemical Engineering at the University of Cambridge. He is also the CEO and CTO of the spin-out company, Cambridge Simulation Solutions LTD. Walter Kähm, a former PhD student under Vassilios S. Vassiliadis, is a process engineer in the chemical sector. Ehecatl Antonio del Rio-Chanona is a lecturer and head of the optimization and machine learning for the process systems engineering group in the Department of Chemical Engineering and the Centre for Process Systems Engineering (CPSE) at Imperial College London. Ye Yuan is currently a professor at Huazhong University of Science and Technology.
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