A new primal-dual interior-point method for semidefinite optimization based on a parameterized kernel function

2020 ◽  
Author(s):  
Mengmeng Li ◽  
Mingwang Zhang ◽  
Kun Huang ◽  
Zhengwei Huang
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Semidefinite Optimization ◽  
Primal Dual

Primal–dual interior-point method for linear optimization based on a kernel function with trigonometric growth term

Optimization ◽  
2018 ◽  
Vol 67 (10) ◽  
pp. 1605-1630 ◽  
Author(s):  
S. Fathi-Hafshejani ◽  
H. Mansouri ◽  
M. Reza Peyghami ◽  
S. Chen
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Interior Point Method ◽  
Linear Optimization ◽  
Point Method ◽  
Primal Dual

New complexity analysis of a full Nesterov–Todd step interior-point method for semidefinite optimization

2017 ◽  
Vol 10 (04) ◽  
pp. 1750070 ◽  
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Complexity Analysis ◽  
Optimization Problems ◽  
Path Following ◽  
Point Method ◽  
Semidefinite Optimization ◽  
Line Searches ◽  
Complexity Result ◽  
Primal Dual

In this paper, we propose a new primal-dual path-following interior-point method for semidefinite optimization based on a new reformulation of the nonlinear equation of the system which defines the central path. The proposed algorithm takes only full Nesterov and Todd steps and therefore no line-searches are needed for generating the new iterations. The convergence of the algorithm is established and the complexity result coincides with the best-known iteration bound for semidefinite optimization problems.

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