Improved Complexity Analysis of Full Nesterov–Todd Step Feasible Interior-Point Method for Symmetric Optimization

G. Q. Wang; L. C. Kong; J. Y. Tao; G. Lesaja

doi:10.1007/s10957-014-0696-2

Improved Complexity Analysis of Full Nesterov–Todd Step Feasible Interior-Point Method for Symmetric Optimization

G. Q. Wang, L. C. Kong, J. Y. Tao, G. Lesaja

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

In this paper, an improved complexity analysis of full Nesterov–Todd step feasible interior-point method for symmetric optimization is considered. Specifically, we establish a sharper quadratic convergence result using several new results from Euclidean Jordan algebras, which leads to a wider quadratic convergence neighbourhood of the central path for the iterates in the algorithm. Furthermore, we derive the currently best known iteration bound for full Nesterov–Todd step feasible interior-point method.

Original language	English
Pages (from-to)	588-604
Number of pages	17
Journal	Journal of Optimization Theory and Applications
Volume	166
Issue number	2
DOIs	https://doi.org/10.1007/s10957-014-0696-2
State	Published - Aug 25 2015

Scopus Subject Areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

Keywords

Euclidean Jordan algebras
Full Nesterov–Todd step
Interior-point methods
Linear optimization over symmetric cones
Polynomial complexity

Access to Document

10.1007/s10957-014-0696-2

Cite this

@article{2a929ff511cb4129bf456e28c7372d2d,

title = "Improved Complexity Analysis of Full Nesterov–Todd Step Feasible Interior-Point Method for Symmetric Optimization",

abstract = "In this paper, an improved complexity analysis of full Nesterov–Todd step feasible interior-point method for symmetric optimization is considered. Specifically, we establish a sharper quadratic convergence result using several new results from Euclidean Jordan algebras, which leads to a wider quadratic convergence neighbourhood of the central path for the iterates in the algorithm. Furthermore, we derive the currently best known iteration bound for full Nesterov–Todd step feasible interior-point method.",

keywords = "Euclidean Jordan algebras, Full Nesterov–Todd step, Interior-point methods, Linear optimization over symmetric cones, Polynomial complexity",

author = "Wang, \{G. Q.\} and Kong, \{L. C.\} and Tao, \{J. Y.\} and G. Lesaja",

note = "Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media New York.",

year = "2015",

month = aug,

day = "25",

doi = "10.1007/s10957-014-0696-2",

language = "English",

volume = "166",

pages = "588--604",

journal = "Journal of Optimization Theory and Applications",

issn = "0022-3239",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Improved Complexity Analysis of Full Nesterov–Todd Step Feasible Interior-Point Method for Symmetric Optimization

AU - Wang, G. Q.

AU - Kong, L. C.

AU - Tao, J. Y.

AU - Lesaja, G.

PY - 2015/8/25

Y1 - 2015/8/25

N2 - In this paper, an improved complexity analysis of full Nesterov–Todd step feasible interior-point method for symmetric optimization is considered. Specifically, we establish a sharper quadratic convergence result using several new results from Euclidean Jordan algebras, which leads to a wider quadratic convergence neighbourhood of the central path for the iterates in the algorithm. Furthermore, we derive the currently best known iteration bound for full Nesterov–Todd step feasible interior-point method.

AB - In this paper, an improved complexity analysis of full Nesterov–Todd step feasible interior-point method for symmetric optimization is considered. Specifically, we establish a sharper quadratic convergence result using several new results from Euclidean Jordan algebras, which leads to a wider quadratic convergence neighbourhood of the central path for the iterates in the algorithm. Furthermore, we derive the currently best known iteration bound for full Nesterov–Todd step feasible interior-point method.

KW - Euclidean Jordan algebras

KW - Full Nesterov–Todd step

KW - Interior-point methods

KW - Linear optimization over symmetric cones

KW - Polynomial complexity

UR - https://www.scopus.com/pages/publications/84937939954

U2 - 10.1007/s10957-014-0696-2

DO - 10.1007/s10957-014-0696-2

M3 - Article

SN - 0022-3239

VL - 166

SP - 588

EP - 604

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 2

ER -

Improved Complexity Analysis of Full Nesterov–Todd Step Feasible Interior-Point Method for Symmetric Optimization

Abstract

Scopus Subject Areas

Keywords

Access to Document

Other files and links

Fingerprint

Cite this