Imperial College London
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ProfessorThomasParisini

Faculty of Engineering, Department of Electrical and Electronic Engineering

Chair in Industrial Control, Head of Group for CAP
 
 
 
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Contact

 

+44 (0)20 7594 6240t.parisini Website

 
 
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Location

 

1114Electrical EngineeringSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@inbook{Zoppoli:2020:10.1007/978-3-030-29693-3_2,
author = {Zoppoli, R and Sanguineti, M and Gnecco, G and Parisini, T},
booktitle = {Communications and Control Engineering},
doi = {10.1007/978-3-030-29693-3_2},
pages = {39--88},
title = {From functional optimization to nonlinear programming by the extended ritz method},
url = {http://dx.doi.org/10.1007/978-3-030-29693-3_2},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - CHAP
AB  - This chapter describes the approximate solution of infinite-dimensional optimization problems by the “Extended Ritz Method” (ERIM). The ERIM consists in substituting the admissible functions with fixed-structure parametrized (FSP) functions containing vectors of “free” parameters. The larger the dimensions, the more accurate the approximations of the optimal solutions of the original functional optimization problems. This requires solving easier nonlinear programming problems. In the area of function approximation, we review the definition of approximating sequences of sets, which enjoy the property of density in the sets of functions one wants to approximate. Then, we provide the definition of polynomially complex approximating sequences of sets, which are able to approximate functions provided with suitable regularity properties by using, for a desired arbitrary accuracy, a number of “free” parameters increasing at most polynomially when the number of function arguments grows. In the less studied area of approximate solution of infinite-dimensional optimization problems, the optimizing sequences and the polynomially complex optimizing sequences of FSP functions are defined. Results are presented that allow to conclude that, if appropriate hypotheses occur, polynomially complex approximating sequences of sets give rise to polynomially complex optimizing sequences of FSP functions, possibly mitigating the curse of dimensionality.
AU  - Zoppoli,R
AU  - Sanguineti,M
AU  - Gnecco,G
AU  - Parisini,T
DO  - 10.1007/978-3-030-29693-3_2
EP  - 88
PY  - 2020///
SP  - 39
TI  - From functional optimization to nonlinear programming by the extended ritz method
T1  - Communications and Control Engineering
UR  - http://dx.doi.org/10.1007/978-3-030-29693-3_2
ER  -
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