Complexity analysis of infeasible interior-point method for semidefinite optimization based on a new trigonometric kernel function

2018 ◽  
Vol 13 (1) ◽  
pp. 127-145
Author(s):  
M. Moslemi ◽  
B. Kheirfam
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Interior Point Method ◽  
Complexity Analysis ◽  
Point Method ◽  
Semidefinite Optimization ◽  
Infeasible Interior Point Method

Full-NT step infeasible interior-point method for SOCO based on a specific kernel function

2013 ◽  
Vol 25 (3) ◽  
pp. 549-565 ◽  
Author(s):  
S. Bouali ◽  
S. Kabbaj
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Infeasible Interior Point Method

An improved and modified infeasible interior-point method for symmetric optimization

2016 ◽  
Vol 09 (03) ◽  
pp. 1650059 ◽  
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Interior Point Methods ◽  
Linear Optimization ◽  
Point Method ◽  
Semidefinite Optimization ◽  
Symmetric Optimization ◽  
Second Order Cone ◽  
Iteration Bound ◽  
Infeasible Interior Point Method

In this paper an improved and modified version of full Nesterov–Todd step infeasible interior-point methods for symmetric optimization published in [A new infeasible interior-point method based on Darvay’s technique for symmetric optimization, Ann. Oper. Res. 211(1) (2013) 209–224; G. Gu, M. Zangiabadi and C. Roos, Full Nesterov–Todd step infeasible interior-point method for symmetric optimization, European J. Oper. Res. 214(3) (2011) 473–484; Simplified analysis of a full Nesterov–Todd step infeasible interior-point method for symmetric optimization, Asian-Eur. J. Math. 8(4) (2015) 1550071, 14 pp.] is considered. Each main iteration of our algorithm consisted of only a feasibility step, whereas in the earlier versions each iteration is composed of one feasibility step and several — at most three — centering steps. The algorithm finds an [Formula: see text]-solution of the underlying problem in polynomial-time and its iteration bound improves the earlier bounds factor from [Formula: see text] and [Formula: see text] to [Formula: see text]. Moreover, our method unifies the analysis for linear optimization, second-order cone optimization and semidefinite optimization.

Sign in / Sign up

Export Citation Format

Share Document