An arc-search infeasible interior-point method for semidefinite optimization with the negative infinity neighborhood

• Published in: Numerical algorithms Vol. 88; no. 1; pp. 143 - 163
• Main Authors: Kheirfam, Behrouz, Osmanpour, Naser, Keyanpour, Mohammad
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2021; Springer Nature B.V
• Subjects: Algebra; Algorithms; Approximation; Computer Science; Euclidean space; Infinity; Iterative methods; Neighborhoods; Numeric Computing; Numerical Analysis; Optimization; Original Paper; Searching; Theory of Computation; Semidefinite optimization; Polynomial complexity; 90C51; Arc-search strategy; 90C22; Infeasible interior-point method
• ISSN: 1017-1398; 1572-9265
• DOI: 10.1007/s11075-020-01033-1

We present an arc-search infeasible interior-point algorithm for semidefinite optimization using the Nesterov-Todd search directions. The algorithm is based on the negative infinity neighborhood of the central path. The algorithm searches an ε -approximate solution of the problem along the ellipsoidal approximation of the entire central path. The convergence analysis of the algorithm is presented and shows that the algorithm has the iteration complexity bound O n 3 / 2 log ε − 1 . Here, n is the dimension of the problem and ε is the required precision. The numerical results show that our algorithm is efficient and promising.