Book contents
- Frontmatter
- Contents
- Notation
- Preface
- Part I Overview of Optimization:Applications and Problem Formulations
- Part II From General Mathematical Background to General Nonlinear Programming Problems (NLP)
- Part III Formulation and Solution of Linear Programming (LP) Problems
- 10 Introduction to LP Models
- 11 Numerical Solution of LP Problems Using the Simplex Method
- 12 A Sampler of LP Problem Formulations
- 13 Regression Revisited: Using LP to Fit Linear Models
- 14 Network Flow Problems
- 15 LP and Sensitivity Analysis, in Brief
- 16 Multiobjective Optimization
- 17 Optimization under Uncertainty
- 18 Mixed-Integer Programming Problems
- 19 Global Optimization
- 20 Optimal Control Problems (Dynamic Optimization)
- 21 System Identification and Model Predictive Control
- Index
11 - Numerical Solution of LP Problems Using the Simplex Method
from Part III - Formulation and Solution of Linear Programming (LP) Problems
Published online by Cambridge University Press: 17 December 2020
- Frontmatter
- Contents
- Notation
- Preface
- Part I Overview of Optimization:Applications and Problem Formulations
- Part II From General Mathematical Background to General Nonlinear Programming Problems (NLP)
- Part III Formulation and Solution of Linear Programming (LP) Problems
- 10 Introduction to LP Models
- 11 Numerical Solution of LP Problems Using the Simplex Method
- 12 A Sampler of LP Problem Formulations
- 13 Regression Revisited: Using LP to Fit Linear Models
- 14 Network Flow Problems
- 15 LP and Sensitivity Analysis, in Brief
- 16 Multiobjective Optimization
- 17 Optimization under Uncertainty
- 18 Mixed-Integer Programming Problems
- 19 Global Optimization
- 20 Optimal Control Problems (Dynamic Optimization)
- 21 System Identification and Model Predictive Control
- Index
Summary
The chapter aims to introduce completely the theory behind the simplex method for Linear Programming, by building slowly the material from the solution set of rectangular linear (affine) systems of equations to vertex solutions.The simplex method is introduced as a natural way to progress from one vertex to the next, on the constraint polytope, always improving the objective until the optimal solution is reached.Use of artificial variables and the two-phase simplex method is made to deal with finding an initial feasible basis for the simplex method.Pathological cases of LP problems are also considered, and how the simplex method would detect them is highlighted.
Keywords
- Type
- Chapter
- Information
- Optimization for Chemical and Biochemical EngineeringTheory, Algorithms, Modeling and Applications, pp. 123 - 132Publisher: Cambridge University PressPrint publication year: 2021