A modified infeasible interior-point algorithm with full-Newton step for semidefinite optimization

ABSTRACT

Recently, Mansouri et al. (J. Optim. Theory Appl. 166: 605-618, 2015) presented an improved infeasible interior-point algorithm for linear optimization. Their algorithm has the shortcoming that the proximity measure may be still large when the duality gap approaches to zero. In this paper, we propose an infeasible interior-point algorithm for semidefinite optimization with a modified search direction. This modification is an attempt to decrease the value of the proximity measure, which is important to determine whether or not to perform centreing steps in the classical infeasible interior-point algorithms. Some preliminary numerical results show the benefit of the proposed algorithm as well.

KEYWORDS:

• Semidefinite optimization
• infeasible interior-point algorithm
• full-Newton step
• Kernel function
• polynomial complexity

AMS CLASSIFICATIONS:

• 65K05
• 90C22
• 90C51

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by National Natural Science Foundation of China (Grant No. 61179040) and Natural Science Basis Research Plan in Shaanxi Province of China (Program No. 2017JM1014).