Nonlinear systems and optimization for the chemical engineer : solving numerical problems /: solving numerical problems. (2013)

• Record Type: Book
• Further Information: Note: Guido Buzzi-Ferraris, Flavio Manenti.
• Authors: Buzzi-Ferraris, G (Guido); Manenti, Flavio
• Contents: Preface; ; FUNCTION ROOT-FINDING; Introduction; Substitution Algorithms; Bolzano's Algorithm; Function Approximation; Use of a Multiprocessor Machine with a Known Interval of Uncertainty; Search for an Interval of Uncertainty; Stop Criteria; Classes for Function Root-Finding; Case Studies; Tests for BzzFunctionRoot and BzzFunctionRootMP Classes; Some Caveats; ; ONE-DIMENSIONAL OPTIMIZATION; Introduction; Measuring the Efficiency of the Search for the Minimum; Comparison Methods; Parabolic Interpolation; Cubic Interpolation; Gradient-Based Methods; Combination of Algorithms in a General Program; Parallel Computations; Search for the Interval of Uncertainty; Stop Criteria; Classes for One-Dimensional Minimization; Case Studies; Tests; ; UNCONSTRAINED OPTIMIZATION; Introduction; Heuristic Methods; Gradient-Based Methods; Conjugate Direction Methods; Newton's Method; Modified Newton Methods; Quasi-Newton Methods; Narrow Valley Effect; Stop Criteria; BzzMath Classes for Unconstrained Multidimensional Minimization; Case Study; Tests; ; LARGE-SCALE UNCONSTRAINED OPTIMIZATION; Introduction; Collecting a Sparse Symmetric Matrix; Ordering the Hessian Rows and Columns; Quadratic Functions; Hessian Evaluation; Newton's Method; Inexact Newton Methods; Practical Preconditioners; openMP Parallelization; Class for Large-Scale Unconstrained Minimization; ; ROBUST UNCONSTRAINED MINIMIZATION; Introduction; One-Dimensional Minimization; Classes for One-Dimensional Robust Minimization; Examples in One-Dimensional Space; Examples in Multidimensional Space; Two-Dimensional Space; Classes for Robust Two-Dimensional Minimization; Examples for BzzMinimizationTwoVeryRobust Class; Multidimensional Robust Minimization; Class for Robust Multidimensional Minimization; ; ROBUST FUNCTION ROOT-FINDING; Introduction; Class and Examples; ; NONLINEAR SYSTEMS; Introduction; Comparing Nonlinear Systems to Other Iterative Problems; Convergence Test; Substitution Methods; Minimization Methods; Jacobian Evaluation; Newton's Method; Gauss-Newton Method; Modified Newton Methods; Newton's Method and Parallel Computations; Quasi-Newton Methods; Quasi-Newton Methods and Parallel Computing; Stop Criteria; Classes for Nonlinear System Solution with Dense Matrices; Tests for the BzzNonLinearSystem Class; Sparse and Large-Scale Systems; Large Linear System Solution with Iterative Methods; Classes for Nonlinear System Solution with Sparse Matrices; Continuation Methods; Solution of Certain Equations with Respect to Certain Variables; Case Studies; Special Cases; Some Caveats; ; UNDERDIMENSIONED NONLINEAR SYSTEMS; Introduction; Underdimensioned Linear Systems; Class for Underdimensioned Nonlinear System Solution; ; CONSTRAINED MINIMIZATION; Introduction; Equality Constraints; Equality and Inequality Constraints; Lagrangian Dual Problem; ; LINEAR PROGRAMMING; Introduction; Basic Attic Method Concepts; Attic Method; Differences between the Attic Method and Traditional Approaches; Explosion in the Number of Iterations; Degeneracy; Duality; General Considerations; ; QUADRATIC PROGRAMMING; Introduction; KKT Conditions for a QP Problem; Equality-Constrained QP; Equality- and Inequality-Constrained Problems; Class for QP; Projection or Reduced Direction Search Methods for Bound-Constrained Problems; Equality, Inequality, and Bound Constraints; Tests; ; CONSTRAINED MINIMIZATION: PENALTY AND BARRIER FUNCTIONS; Introduction; Penalty Function Methods; Barrier Function Methods; Mixed Penalty-Barrier Function Methods; ; CONSTRAINED MINIMIZATION: ACTIVE SET METHODS; Introduction; Class for Constrained Minimization; Successive Linear Programming; Projection Methods; Reduced Direction Search Methods; Projection or Reduced Direction Search Methods for Bound-Constrained Problems; Successive Quadratic Programming or Projected Lagrangian Method; Narrow Valley Effect; The Nonlinear Constraints Effect; Tests; ; PARAMETRIC CONTINUATION IN OPTIMIZATION AND PROCESS CONTROL; Introduction; Algebraic Constraints; ;
• Publisher Details: Place of publication not identified : Wiley-VCH
• Publication Date: 2013
• Extent: 1 online resource (522 pages)
• Subjects: 518; Numerical analysis; Mathematical optimization; Nonlinear systems
• Languages: English
• ISBNs: 9783527667161
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.