Singularities in minimax optimization of networks

Kaj Madsen; Hans Schjær-Jacobsen

doi:10.1109/TCS.1976.1084240

Singularities in minimax optimization of networks

Kaj Madsen, Hans Schjær-Jacobsen

Research output: Contribution to journal › Journal article › Research › peer-review

407 Downloads (Pure)

Abstract

A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and singular problems, is presented. A theorem for determining a singularity that is present in a given problem is formulated. A group of problems often used in the literature to test nonlinear minimax algorithms, i.e., minimax design of multisection quarter-wave transformers, is shown to exhibit singularities and the reason for this is pointed out. Based on the theoretical results presented an algorithm for nonlinear minimax optimization is developed. The new algorithm maintains the quadratic convergence property of a recent algorithm by Madsen et al. when applied to regular problems and it is demonstrated to significantly improve the final convergence on singular problems.

Original language	English
Journal	IEEE Transactions on Circuits and Systems
Volume	23
Issue number	7
Pages (from-to)	456-460
ISSN	0098-4094
DOIs	https://doi.org/10.1109/TCS.1976.1084240
Publication status	Published - 1976

Bibliographical note

Copyright: 1976 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

Access to Document

10.1109/TCS.1976.1084240

JacobFinal published version, 510 KB

OpenUrl availability

Full text

Cite this

@article{3967c407cc044cda9df173d6ad9de020,

title = "Singularities in minimax optimization of networks",

abstract = "A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and singular problems, is presented. A theorem for determining a singularity that is present in a given problem is formulated. A group of problems often used in the literature to test nonlinear minimax algorithms, i.e., minimax design of multisection quarter-wave transformers, is shown to exhibit singularities and the reason for this is pointed out. Based on the theoretical results presented an algorithm for nonlinear minimax optimization is developed. The new algorithm maintains the quadratic convergence property of a recent algorithm by Madsen et al. when applied to regular problems and it is demonstrated to significantly improve the final convergence on singular problems.",

author = "Kaj Madsen and Hans Schj{\ae}r-Jacobsen",

note = "Copyright: 1976 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE",

year = "1976",

doi = "10.1109/TCS.1976.1084240",

language = "English",

volume = "23",

pages = "456--460",

journal = "IEEE Transactions on Circuits and Systems",

issn = "0098-4094",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "7",

}

TY - JOUR

T1 - Singularities in minimax optimization of networks

AU - Madsen, Kaj

AU - Schjær-Jacobsen, Hans

N1 - Copyright: 1976 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

PY - 1976

Y1 - 1976

N2 - A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and singular problems, is presented. A theorem for determining a singularity that is present in a given problem is formulated. A group of problems often used in the literature to test nonlinear minimax algorithms, i.e., minimax design of multisection quarter-wave transformers, is shown to exhibit singularities and the reason for this is pointed out. Based on the theoretical results presented an algorithm for nonlinear minimax optimization is developed. The new algorithm maintains the quadratic convergence property of a recent algorithm by Madsen et al. when applied to regular problems and it is demonstrated to significantly improve the final convergence on singular problems.

AB - A theoretical treatment of singularities in nonlinear minimax optimization problems, which allows for a classification in regular and singular problems, is presented. A theorem for determining a singularity that is present in a given problem is formulated. A group of problems often used in the literature to test nonlinear minimax algorithms, i.e., minimax design of multisection quarter-wave transformers, is shown to exhibit singularities and the reason for this is pointed out. Based on the theoretical results presented an algorithm for nonlinear minimax optimization is developed. The new algorithm maintains the quadratic convergence property of a recent algorithm by Madsen et al. when applied to regular problems and it is demonstrated to significantly improve the final convergence on singular problems.

U2 - 10.1109/TCS.1976.1084240

DO - 10.1109/TCS.1976.1084240

M3 - Journal article

SN - 0098-4094

VL - 23

SP - 456

EP - 460

JO - IEEE Transactions on Circuits and Systems

JF - IEEE Transactions on Circuits and Systems

IS - 7

ER -

Singularities in minimax optimization of networks

Abstract

Bibliographical note

Access to Document

OpenUrl availability

Fingerprint

Cite this