Nonlinear systems and optimization for the chemical engineer : solving numerical problems için kapak resmi
Başlık:
Nonlinear systems and optimization for the chemical engineer : solving numerical problems
Dil:
English
ISBN:
9783527667147

9783527667178

9781306140713
Yayın Bilgileri:
Weinheim :

Wiley-VCH,

2013.
Fiziksel Tanımlama:
1 online resource.
İçerik:
Nonlinear Systems and Optimization for the Chemical Engineer: Solving Numerical Problems; Contents; Preface; 1 Function Root-Finding; 1.1 Introduction; 1.2 Substitution Algorithms; 1.3 Bolzano's Algorithm; 1.4 Function Approximation; 1.4.1 Newton's Method; 1.4.2 The Secant Method; 1.4.3 Regula Falsi Method; 1.4.4 Muller's Method or Parabolic Interpolation; 1.4.5 Hyperbolic Interpolation Method; 1.4.6 Inverse Polynomial Interpolation Method; 1.4.7 Inverse Rational Interpolation Method; 1.5 Use of a Multiprocessor Machine with a Known Interval of Uncertainty.

1.6 Search for an Interval of Uncertainty1.7 Stop Criteria; 1.8 Classes for Function Root-Finding; 1.9 Case Studies; 1.9.1 Calculation of the Volume of a Nonideal Gas; 1.9.2 Calculation of the Bubble Point of Vapor-Liquid Equilibrium; 1.9.3 Zero-Crossing Problem; 1.9.4 Stationary Condition in a Gravity-Flow Tank; 1.10 Tests for BzzFunctionRoot and BzzFunctionRootMP Classes; 1.11 Some Caveats; 2 One-Dimensional Optimization; 2.1 Introduction; 2.2 Measuring the Efficiency of the Search for the Minimum; 2.3 Comparison Methods; 2.4 Parabolic Interpolation; 2.5 Cubic Interpolation.

2.6 Gradient-Based Methods2.7 Combination of Algorithms in a General Program; 2.8 Parallel Computations; 2.9 Search for the Interval of Uncertainty; 2.10 Stop Criteria; 2.11 Classes for One-Dimensional Minimization; 2.12 Case Studies; 2.12.1 Optimization of Unimodal Functions; 2.12.2 Optimization of a Batch Reactor; 2.12.3 Maximum Level in a Gravity-Flow Tank in Transient Conditions; 2.13 Tests; 3 Unconstrained Optimization; 3.1 Introduction; 3.1.1 Necessary and Sufficient Conditions; 3.1.2 Quadratic Functions; 3.1.3 Directions of Function Decrease.

3.1.4 Comparison with the One-Dimensional Case3.1.5 Classification of Methods; 3.2 Heuristic Methods; 3.2.1 Modified Hooke-Jeeves Method; 3.2.2 The Rosenbrock Method; 3.2.3 The Nelder-Mead Simplex Method; 3.2.4 Robust Optnov Method Combined with the Simplex Method; 3.3 Gradient-Based Methods; 3.4 Conjugate Direction Methods; 3.5 Newton's Method; 3.6 Modified Newton Methods; 3.6.1 Singular or Nonpositive Definite Hessian Matrix; 3.6.2 Convergence Problems; 3.6.3 One-Dimensional Search; 3.6.4 Trust Region Methods; 3.6.5 Use of Alternative Methods; 3.7 Quasi-Newton Methods.

3.8 Narrow Valley Effect3.9 Stop Criteria; 3.10 BzzMath Classes for Unconstrained Multidimensional Minimization; 3.11 Case Study; 3.11.1 Optimization of a Batch Reactor; 3.11.2 Optimal Adiabatic Bed Reactors for Sulfur Dioxide with Cold Shot Cooling; 3.11.3 Global Optimization; 3.12 Tests; 4 Large-Scale Unconstrained Optimization; 4.1 Introduction; 4.2 Collecting a Sparse Symmetric Matrix; 4.3 Ordering the Hessian Rows and Columns; 4.4 Quadratic Functions; 4.5 Hessian Evaluation; 4.6 Newton's Method; 4.7 Inexact Newton Methods; 4.8 Practical Preconditioners; 4.9 openMP Parallelization.
Özet:
This third in a suite of four practical guides is an engineer's companion to using numerical methods for the solution of complex mathematical problems. It explains the theory behind current numerical methods and shows in a step-by-step fashion how to use them. The volume focuses on optimization from experimental to large-scale processes, detailing the algorithms needed to solve real-life problems. It describes the methods, innovative techniques and strategies that are all implemented in a well-established, freeware mathematical toolbox called BzzMath, which is developed and maintained by the au.
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Özet

This third book in a suite of four practical guides is an engineer's companion to using numerical methods for the solution of complex mathematical problems. The required software is provided by way of the freeware mathematical library BzzMath that is developed and maintained by the authors. The present volume focuses on optimization and nonlinear systems solution. The book describes numerical methods, innovative techniques and strategies that are all implemented in a well-established, freeware library. Each of these handy guides enables the reader to use and implement standard numerical tools for their work, explaining the theory behind the various functions and problem solvers, and showcasing applications in diverse scientific and engineering fields. Numerous examples, sample codes, programs and applications are proposed and discussed. The book teaches engineers and scientists how to use the latest and most powerful numerical methods for their daily work.


Özet

This third book in a suite of four practical guides is an engineer's companion to using numerical methods for the solution of complex mathematical problems. The required software is provided by way of the freeware mathematical library BzzMath that is developed and maintained by the authors. The present volume focuses on optimization and nonlinear systems solution. The book describes numerical methods, innovative techniques and strategies that are all implemented in a well-established, freeware library. Each of these handy guides enables the reader to use and implement standard numerical tools for their work, explaining the theory behind the various functions and problem solvers, and showcasing applications in diverse scientific and engineering fields. Numerous examples, sample codes, programs and applications are proposed and discussed. The book teaches engineers and scientists how to use the latest and most powerful numerical methods for their daily work.


Yazar Notları

Guido Buzzi-Ferraris is full professor of process systems engineering at Politecnico di Milano, Italy, where he holds two courses: "Methods and Numerical Applications in Chemical Engineering" and "Regression Models and Statistics". He works on numerical analysis, statistics, differential systems, and optimization. He has authored books of international relevance on numerical analysis, such as "Scientific C++" edited by Addison-Wesley, and over than 200 papers on international magazines. He is the inventor and the developer of BzzMath library, which is currently adopted by academies, R&D groups, and industries. He is permanent member of the "EFCE Working Party - Computer Aided Process Engineering" since 1969 and editorial advisory board of "Computers & Chemical Engineering" since 1987.

Flavio Manenti is assistant professor of chemical engineering at Politecnico di Milano, Italy. He obtained his academic degree and PhD at Politecnico di Milano, where he currently collaborates with Professor Buzzi-Ferraris. He holds courses on "Process Dynamics and Control of Industrial Processes" and "Supply Chain Optimization" and he works on numerical analysis, process control and optimization. He has also received international scientific awards, such as Memorial Burianec (Prague, CZ) and Excellence in Simulation (Lake Forest, CA, USA), for his research activities and scientific publications.


Guido Buzzi-Ferraris is full professor of process systems engineering at Politecnico di Milano, Italy, where he holds two courses: "Methods and Numerical Applications in Chemical Engineering" and "Regression Models and Statistics". He works on numerical analysis, statistics, differential systems, and optimization. He has authored books of international relevance on numerical analysis, such as "Scientific C++" edited by Addison-Wesley, and over than 200 papers on international magazines. He is the inventor and the developer of BzzMath library, which is currently adopted by academies, R&D groups, and industries. He is permanent member of the "EFCE Working Party - Computer Aided Process Engineering" since 1969 and editorial advisory board of "Computers & Chemical Engineering" since 1987.

Flavio Manenti is assistant professor of chemical engineering at Politecnico di Milano, Italy. He obtained his academic degree and PhD at Politecnico di Milano, where he currently collaborates with Professor Buzzi-Ferraris. He holds courses on "Process Dynamics and Control of Industrial Processes" and "Supply Chain Optimization" and he works on numerical analysis, process control and optimization. He has also received international scientific awards, such as Memorial Burianec (Prague, CZ) and Excellence in Simulation (Lake Forest, CA, USA), for his research activities and scientific publications.