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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

Vassilios S. Vassiliadis ,
Walter Kähm ,
Ehecatl Antonio del Rio Chanona  and
Ye Yuan
Vassilios S. Vassiliadis
Affiliation:
University of Cambridge
Ehecatl Antonio del Rio Chanona
Affiliation:
Imperial College London
Ye Yuan
Affiliation:
Huazhong University of Science and Technology
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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.

Keywords

Quadratic functionsConvexityLeast Squares Fitting
Type
Chapter
Information
Optimization for Chemical and Biochemical Engineering
Theory, Algorithms, Modeling and Applications
 , pp. 44 - 56
Publisher: Cambridge University Press
Print publication year: 2021

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