Page 7 - Sustainability in the Process Industry Integration and Optimization

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3.3 Optimization: Definition and Mathematical

Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3.1 What Is Optimization? . . . . . . . . . . . . . 25
3.3.2 Mathematical Formulation of
Optimization Problems . . . . . . . . . . . . 25
3.4 Main Classes of Optimization Problems . . . . 26
3.5 Conditions for Optimality . . . . . . . . . . . . . . . . 28
3.5.1 Conditions for Local Optimality . . . . 28
3.5.2 Conditions for Global Optimality . . . 28
3.6 Deterministic Algorithms for Solving Continuous

Linear Optimization Problems . . . . . . . . . . . . . 29

3.7 Deterministic Algorithms for Solving Continuous
Nonlinear Optimization Problems . . . . . . . . . . 29
3.7.1 Search Algorithms for Nonlinear
Unconstrained Problems . . . . . . . . . . . 30
3.7.2 Algorithms for Solving Constrained
Nonlinear Problems . . . . . . . . . . . . . . . 31
3.8 Deterministic Methods for Solving
Discrete Problems . . . . . . . . . . . . . . . . . . . . . . . . 31
3.9 Stochastic Search Methods for Solving

Optimization Problems . . . . . . . . . . . . . . . . . . . 32
3.10 Creating Models . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.10.1 Conceptual Modeling . . . . . . . . . . . . . 34
3.10.2 Mathematical Modeling of Processes:
Constructing the Equations . . . . . . . . 35
3.10.3 Choosing an Objective Function . . . . 37
3.10.4 Handling Process Complexity . . . . . . 38
3.10.5 Applying Process Insight . . . . . . . . . . 40
3.10.6 Handling Model Nonlinearity . . . . . . 41
3.10.7 Evaluating Model Adequacy and
Precision . . . . . . . . . . . . . . . . . . . . . . . . . 43
4 Process Integration for Improving

Energy Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1 Introduction to Heat Exchange and
Heat Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1.1 Heat Exchange Matches . . . . . . . . . . . . 46
4.1.2 Implementing Heat Exchange
Matches . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Basics of Process Integration . . . . . . . . . . . . . . . 47
4.2.1 Process Integration and Heat
Integration . . . . . . . . . . . . . . . . . . . . . . . 47