Complexity Analysis of an Interior Point Algorithm for the Semidefinite Optimization Based on a Kernel Function with a Double Barrier Term

In this paper, we establish the polynomial complexity of a primal-dual path-following interior point algorithm for solving semidefinite optimization（SDO） problems. The proposed algorithm is based on a new kernel function which differs from the existing kernel functions in which it has a double barri...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series Vol. 31; no. 3; pp. 543 - 556
Main Author: Achache, Mohamed
Format: Journal Article
Language:English
Published: Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.03.2015
Springer Nature B.V
Subjects:
Algorithms
Barriers
Complexity
Eigenvalues
Functions (mathematics)
Kernel functions
Mathematical analysis
Mathematical programming
Mathematics
Mathematics and Statistics
Optimization
Polynomials
Semidefinite programming
Studies
Texts
优化
内核函数
内点算法
复杂性分析
多项式复杂性
屏障
期限
路径跟踪
kernel functions
90C51
65K05
complexity of algorithms
90C25
90C22
Semidefinite optimization
primal-dual interior point methods
large and small-update algorithms
ISSN:1439-8516, 1439-7617
Online Access:Get full text
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Summary:In this paper, we establish the polynomial complexity of a primal-dual path-following interior point algorithm for solving semidefinite optimization（SDO） problems. The proposed algorithm is based on a new kernel function which differs from the existing kernel functions in which it has a double barrier term. With this function we define a new search direction and also a new proximity function for analyzing its complexity. We show that if q1 〉 q2 〉 1, the algorithm has O（（q1 ＋ 1） nq1＋1/2（q1-q2）logn/ε）and O（（q1 ＋ 1）2（q1-q2）^3q1-2q2＋1√n logn/c） complexity results for large- and small-update methods, respectively.
Bibliography:11-2039/O1
Semidefinite optimization, kernel functions, primal-dual interior point methods, large andsmall-update algorithms, complexity of algorithms
In this paper, we establish the polynomial complexity of a primal-dual path-following interior point algorithm for solving semidefinite optimization（SDO） problems. The proposed algorithm is based on a new kernel function which differs from the existing kernel functions in which it has a double barrier term. With this function we define a new search direction and also a new proximity function for analyzing its complexity. We show that if q1 〉 q2 〉 1, the algorithm has O（（q1 ＋ 1） nq1＋1/2（q1-q2）logn/ε）and O（（q1 ＋ 1）2（q1-q2）^3q1-2q2＋1√n logn/c） complexity results for large- and small-update methods, respectively.
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-015-1314-4