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6 - Unconstrained Multivariate Gradient-Based Minimization

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

Unconstrained multivariate gradient-based minimization is introduced by means of search direction-producing methods, focusing on steepest descent and Newton's method.Issues with both methods are discussed, highlighting what happens in the case of locally nonconvex functions, particularly in Newton's method.Linesearch is introduced, effectively rendering multidimensional optimization into a sequence of one-dimensional searches along the ray of the search directions produced.Linesearch criteria are discussed, such as the Armijo first condition, and efficient ways to cut the step size are discussed.

Keywords

Steepest descentNewton's MethodTermination criteriaLinesearch methods
Type
Chapter
Information
Optimization for Chemical and Biochemical Engineering
Theory, Algorithms, Modeling and Applications
 , pp. 63 - 80
Publisher: Cambridge University Press
Print publication year: 2021

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