Nonlinear Systems and Optimization for the Chemical Engineer : Solving Numerical Problems.

By: Buzzi-Ferraris, GuidoContributor(s): Manenti, FlavioPublisher: Weinheim : John Wiley & Sons, Incorporated, 2014Copyright date: ©2014Edition: 1st edDescription: 1 online resource (524 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783527667178Subject(s): Nonlinear systems.;Numerical analysisGenre/Form: Electronic books. Additional physical formats: Print version:: Nonlinear Systems and Optimization for the Chemical Engineer : Solving Numerical ProblemsDDC classification: 660.0151 LOC classification: QA402.B89 2014ebOnline resources: Click to View
Contents:
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 Uncertainty -- 1.7 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 Methods -- 2.7 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 Case.
3.1.5 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 Effect -- 3.9 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 -- 4.10 Class for Large-Scale Unconstrained Minimization -- 5 Robust Unconstrained Minimization -- 5.1 Introduction -- 5.2 One-Dimensional Minimization -- 5.3 Classes for One-Dimensional Robust Minimization -- 5.4 Examples in One-Dimensional Space -- 5.5 Examples in Multidimensional Space -- 5.6 Two-Dimensional Minimization -- 5.7 Classes for Robust Two-Dimensional Minimization -- 5.8 Examples for BzzMinimizationTwoVeryRobust Class -- 5.9 Multidimensional Robust Minimization -- 5.9.1 Outer Optimizer -- 5.9.2 Inner Optimizer -- 5.10 Class for Robust Multidimensional Minimization -- 6 Robust Function Root-Finding -- 6.1 Introduction -- 6.2 Class and Examples -- 7 Nonlinear Systems.
7.1 Introduction -- 7.2 Comparing Nonlinear Systems to Other Iterative Problems -- 7.2.1 Comparison with Function Root-Finding -- 7.2.2 Comparison with the Multidimensional Optimization -- 7.3 Convergence Test -- 7.4 Substitution Methods -- 7.5 Minimization Methods -- 7.6 Jacobian Evaluation -- 7.7 Newton's Method -- 7.8 Gauss-Newton Method -- 7.9 Modified Newton Methods -- 7.9.1 Singular or Ill-Conditioned Jacobian -- 7.9.2 Convergence Problem -- 7.10 Newton's Method and Parallel Computations -- 7.11 Quasi-Newton Methods -- 7.12 Quasi-Newton Methods and Parallel Computing -- 7.13 Stop Criteria -- 7.13.1 Bounds, Constraints, and Discontinuities -- 7.14 Classes for Nonlinear System Solution with Dense Matrices -- 7.15 Tests for the BzzNonLinearSystem Class -- 7.16 Sparse and Large-Scale Systems -- 7.17 Large Linear System Solution with Iterative Methods -- 7.18 Classes for Nonlinear System Solution with Sparse Matrices -- 7.19 Continuation Methods -- 7.20 Solution of Certain Equations with Respect to Certain Variables -- 7.21 Case Studies -- 7.21.1 Heat Exchange in a Thermal Furnace -- 7.21.2 Calculation of Chemical Equilibria -- 7.21.3 Multiple Solutions in a CSTR -- 7.21.4 Critical Size of a Nuclear Reactor -- 7.21.5 Stationary Conditions for a Nonisothermal Continuous Stirred Tank Reactor -- 7.21.6 Vapor-Liquid Equilibrium: The Flash Separator -- 7.21.7 Boundary Value Problems -- 7.22 Special Cases -- 7.22.1 Vapor-Liquid Equilibrium: Distillation Column -- 7.22.2 Kinetic Postprocessor -- 7.23 Some Caveats -- 8 Underdimensioned Nonlinear Systems -- 8.1 Introduction -- 8.2 Underdimensioned Linear Systems -- 8.2.1 Null Space -- 8.2.2 Determination of One Solution -- 8.2.3 Projection Methods -- 8.2.4 Stable Gauss Factorization -- 8.3 Class for Underdimensioned Nonlinear System Solution -- 9 Constrained Minimization -- 9.1 Introduction.
9.2 Equality Constraints -- 9.3 Equality and Inequality Constraints -- 9.4 Lagrangian Dual Problem -- 10 Linear Programming -- 10.1 Introduction -- 10.2 Basic Attic Method Concepts -- 10.3 Attic Method -- 10.3.1 Certain Important Peculiarities of the Attic Method -- 10.3.2 What Happens in a Generic Iteration -- 10.3.3 Selecting the New Feasible Point and the New Inequality Constraint -- 10.3.4 Selection of the Search Direction -- 10.4 Differences between the Attic Method and Traditional Approaches -- 10.4.1 A Simple Application of the Attic Method -- 10.4.2 Certain Advantages to the Attic Method -- 10.5 Explosion in the Number of Iterations -- 10.5.1 Selecting Constraints Rather Than Vertices -- 10.5.2 The Tile Effect -- 10.5.3 Wall Constraints and Roof Constraints -- 10.5.4 When a Constraint with λ>0 Should also be Removed -- 10.6 Degeneracy -- 10.7 Duality -- 10.8 General Considerations -- 11 Quadratic Programming -- 11.1 Introduction -- 11.2 KKT Conditions for a QP Problem -- 11.3 Equality-Constrained QP -- 11.3.1 Solving the Full KKT System -- 11.3.2 Shur-Complement Method -- 11.3.3 Null Space Methods -- 11.4 Equality- and Inequality-Constrained Problems -- 11.5 Class for QP -- 11.6 Projection or Reduced Direction Search Methods for Bound-Constrained Problems -- 11.7 Equality, Inequality, and Bound Constraints -- 11.8 Tests -- 12 Constrained Minimization: Penalty and Barrier Functions -- 12.1 Introduction -- 12.2 Penalty Function Methods -- 12.2.1 Quadratic Penalty Function -- 12.2.2 Nonsmooth Exact Penalty Function -- 12.2.3 The Maratos Effect -- 12.2.4 Augmented Lagrangian Penalty Function -- 12.2.5 Bound-Constrained Formulation for Lagrangian Penalty Function -- 12.3 Barrier Function Methods -- 12.4 Mixed Penalty-Barrier Function Methods -- 13 Constrained Minimization: Active Set Methods -- 13.1 Introduction.
13.2 Class for Constrained Minimization -- 13.3 Successive Linear Programming -- 13.4 Projection Methods -- 13.5 Reduced Direction Search Methods -- 13.6 Projection or Reduced Direction Search Methods for Bound-Constrained Problems -- 13.7 Successive Quadratic Programming or Projected Lagrangian Method -- 13.7.1 Selection of the Merit Function -- 13.7.2 Updating the Jacobian of the System -- 13.8 Narrow Valley Effect -- 13.9 The Nonlinear Constraints Effect -- 13.10 Tests -- 14 Parametric Continuation in Optimization and Process Control -- 14.1 Introduction -- 14.2 Algebraic Constraints -- 14.2.1 Distillation Column -- References -- Appendix A: Copyrights -- Index.
Summary: 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.
Holdings
Item type Current library Call number Status Date due Barcode Item holds
Ebrary Ebrary Afghanistan
Available EBKAF00087447
Ebrary Ebrary Algeria
Available
Ebrary Ebrary Cyprus
Available
Ebrary Ebrary Egypt
Available
Ebrary Ebrary Libya
Available
Ebrary Ebrary Morocco
Available
Ebrary Ebrary Nepal
Available EBKNP00087447
Ebrary Ebrary Sudan

Access a wide range of magazines and books using Pressreader and Ebook central.

Enjoy your reading, British Council Sudan.

Available
Ebrary Ebrary Tunisia
Available
Total holds: 0

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 Uncertainty -- 1.7 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 Methods -- 2.7 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 Case.

3.1.5 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 Effect -- 3.9 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 -- 4.10 Class for Large-Scale Unconstrained Minimization -- 5 Robust Unconstrained Minimization -- 5.1 Introduction -- 5.2 One-Dimensional Minimization -- 5.3 Classes for One-Dimensional Robust Minimization -- 5.4 Examples in One-Dimensional Space -- 5.5 Examples in Multidimensional Space -- 5.6 Two-Dimensional Minimization -- 5.7 Classes for Robust Two-Dimensional Minimization -- 5.8 Examples for BzzMinimizationTwoVeryRobust Class -- 5.9 Multidimensional Robust Minimization -- 5.9.1 Outer Optimizer -- 5.9.2 Inner Optimizer -- 5.10 Class for Robust Multidimensional Minimization -- 6 Robust Function Root-Finding -- 6.1 Introduction -- 6.2 Class and Examples -- 7 Nonlinear Systems.

7.1 Introduction -- 7.2 Comparing Nonlinear Systems to Other Iterative Problems -- 7.2.1 Comparison with Function Root-Finding -- 7.2.2 Comparison with the Multidimensional Optimization -- 7.3 Convergence Test -- 7.4 Substitution Methods -- 7.5 Minimization Methods -- 7.6 Jacobian Evaluation -- 7.7 Newton's Method -- 7.8 Gauss-Newton Method -- 7.9 Modified Newton Methods -- 7.9.1 Singular or Ill-Conditioned Jacobian -- 7.9.2 Convergence Problem -- 7.10 Newton's Method and Parallel Computations -- 7.11 Quasi-Newton Methods -- 7.12 Quasi-Newton Methods and Parallel Computing -- 7.13 Stop Criteria -- 7.13.1 Bounds, Constraints, and Discontinuities -- 7.14 Classes for Nonlinear System Solution with Dense Matrices -- 7.15 Tests for the BzzNonLinearSystem Class -- 7.16 Sparse and Large-Scale Systems -- 7.17 Large Linear System Solution with Iterative Methods -- 7.18 Classes for Nonlinear System Solution with Sparse Matrices -- 7.19 Continuation Methods -- 7.20 Solution of Certain Equations with Respect to Certain Variables -- 7.21 Case Studies -- 7.21.1 Heat Exchange in a Thermal Furnace -- 7.21.2 Calculation of Chemical Equilibria -- 7.21.3 Multiple Solutions in a CSTR -- 7.21.4 Critical Size of a Nuclear Reactor -- 7.21.5 Stationary Conditions for a Nonisothermal Continuous Stirred Tank Reactor -- 7.21.6 Vapor-Liquid Equilibrium: The Flash Separator -- 7.21.7 Boundary Value Problems -- 7.22 Special Cases -- 7.22.1 Vapor-Liquid Equilibrium: Distillation Column -- 7.22.2 Kinetic Postprocessor -- 7.23 Some Caveats -- 8 Underdimensioned Nonlinear Systems -- 8.1 Introduction -- 8.2 Underdimensioned Linear Systems -- 8.2.1 Null Space -- 8.2.2 Determination of One Solution -- 8.2.3 Projection Methods -- 8.2.4 Stable Gauss Factorization -- 8.3 Class for Underdimensioned Nonlinear System Solution -- 9 Constrained Minimization -- 9.1 Introduction.

9.2 Equality Constraints -- 9.3 Equality and Inequality Constraints -- 9.4 Lagrangian Dual Problem -- 10 Linear Programming -- 10.1 Introduction -- 10.2 Basic Attic Method Concepts -- 10.3 Attic Method -- 10.3.1 Certain Important Peculiarities of the Attic Method -- 10.3.2 What Happens in a Generic Iteration -- 10.3.3 Selecting the New Feasible Point and the New Inequality Constraint -- 10.3.4 Selection of the Search Direction -- 10.4 Differences between the Attic Method and Traditional Approaches -- 10.4.1 A Simple Application of the Attic Method -- 10.4.2 Certain Advantages to the Attic Method -- 10.5 Explosion in the Number of Iterations -- 10.5.1 Selecting Constraints Rather Than Vertices -- 10.5.2 The Tile Effect -- 10.5.3 Wall Constraints and Roof Constraints -- 10.5.4 When a Constraint with λ>0 Should also be Removed -- 10.6 Degeneracy -- 10.7 Duality -- 10.8 General Considerations -- 11 Quadratic Programming -- 11.1 Introduction -- 11.2 KKT Conditions for a QP Problem -- 11.3 Equality-Constrained QP -- 11.3.1 Solving the Full KKT System -- 11.3.2 Shur-Complement Method -- 11.3.3 Null Space Methods -- 11.4 Equality- and Inequality-Constrained Problems -- 11.5 Class for QP -- 11.6 Projection or Reduced Direction Search Methods for Bound-Constrained Problems -- 11.7 Equality, Inequality, and Bound Constraints -- 11.8 Tests -- 12 Constrained Minimization: Penalty and Barrier Functions -- 12.1 Introduction -- 12.2 Penalty Function Methods -- 12.2.1 Quadratic Penalty Function -- 12.2.2 Nonsmooth Exact Penalty Function -- 12.2.3 The Maratos Effect -- 12.2.4 Augmented Lagrangian Penalty Function -- 12.2.5 Bound-Constrained Formulation for Lagrangian Penalty Function -- 12.3 Barrier Function Methods -- 12.4 Mixed Penalty-Barrier Function Methods -- 13 Constrained Minimization: Active Set Methods -- 13.1 Introduction.

13.2 Class for Constrained Minimization -- 13.3 Successive Linear Programming -- 13.4 Projection Methods -- 13.5 Reduced Direction Search Methods -- 13.6 Projection or Reduced Direction Search Methods for Bound-Constrained Problems -- 13.7 Successive Quadratic Programming or Projected Lagrangian Method -- 13.7.1 Selection of the Merit Function -- 13.7.2 Updating the Jacobian of the System -- 13.8 Narrow Valley Effect -- 13.9 The Nonlinear Constraints Effect -- 13.10 Tests -- 14 Parametric Continuation in Optimization and Process Control -- 14.1 Introduction -- 14.2 Algebraic Constraints -- 14.2.1 Distillation Column -- References -- Appendix A: Copyrights -- Index.

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.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

There are no comments on this title.

to post a comment.