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)
- 2 General Concepts
- 3 Convexity
- 4 Quadratic Functions
- 5 Minimization in One Dimension
- 6 Unconstrained Multivariate Gradient-Based Minimization
- 7 Constrained Nonlinear Programming Problems (NLP)
- 8 Penalty and Barrier Function Methods
- 9 Interior Point Methods (IPM’s):A Detailed Analysis
- Part III Formulation and Solution of Linear Programming (LP) Problems
- Index
4 - Quadratic Functions
from Part II - From General Mathematical Background to General Nonlinear Programming Problems (NLP)
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)
- 2 General Concepts
- 3 Convexity
- 4 Quadratic Functions
- 5 Minimization in One Dimension
- 6 Unconstrained Multivariate Gradient-Based Minimization
- 7 Constrained Nonlinear Programming Problems (NLP)
- 8 Penalty and Barrier Function Methods
- 9 Interior Point Methods (IPM’s):A Detailed Analysis
- Part III Formulation and Solution of Linear Programming (LP) Problems
- Index
Summary
Quadratic multidimensional functions play a very important role in the understanding of general nonlinear functions. Convexity of quadratic functions is linked in a natural way from its geometrical definition all the way to the properties of its matrix eigenspectrum.Indeed, to second order expansion, and close to the expansion point, any nonlinear function can be approximated by a quadratic – thus providing a crucial link and understanding of the local behaviour and convexity properties of general functions.
- Type
- Chapter
- Information
- Optimization for Chemical and Biochemical EngineeringTheory, Algorithms, Modeling and Applications, pp. 44 - 56Publisher: Cambridge University PressPrint publication year: 2021