Paper Info
Title
A Mehrotra-type predictor-corrector infeasible-interior-point method with a new one-norm neighborhood for symmetric optimization.
Abstract
In this paper, we present a Mehrotra-type predictor-corrector infeasible-interior-point method for symmetric optimization. The proposed algorithm is based on a new one-norm neighborhood, which is an even wider neighborhood than a given negative infinity neighborhood. We are emphatically concerned with the relationship between the one-norm of the Jordan product of x and y and its Frobenius-norm. Based on the relationship, the convergence is shown for a commutative class of search directions. In particular, the complexity bound is O ( r log ε - 1 ) for the Nesterov-Todd search direction, and O ( r 3 / 2 log ε - 1 ) for the x s and s x search direction, where r is the rank of the associated Euclidean Jordan algebra and ε 0 is a given tolerance. To our knowledge, this is the best complexity result obtained so far for infeasible-interior-point methods with a wide neighborhood over symmetric cones. We present a Mehrotra-type predictor-corrector infeasible-IPM with a second order corrector step for symmetric optimization.We prove the important connection ¿ x ¿ y ¿ 1 ¿ 3 ¿ x ¿ F ¿ y ¿ F .The proposed algorithm will restrict the iterates to a new one-norm neighborhood.We obtain the low theoretical complexity bound for the proposed algorithm.
Year
DOI
Venue
2015
10.1016/j.cam.2015.01.027
J. Computational Applied Mathematics
Keywords
Field
DocType
Symmetric cones,Euclidean Jordan algebra,One-norm,Infeasible-interior-point method,Complexity bound
Convergence (routing),Extended real number line,Mathematical optimization,Combinatorics,Commutative property,Mathematical analysis,Euclidean geometry,Iterated function,Predictor–corrector method,Interior point method,Mathematics,Jordan algebra
Journal
Volume
Issue
ISSN
283
C
0377-0427
Citations 
PageRank 
References 
1
0.36
9
Authors
3
Name
Order
Citations
PageRank
Ximei Yang1262.34
Hongwei Liu27812.29
Changhe Liu3383.62