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 \(\mathcal {O}\big (n^{3/2}\log {\varepsilon }^{-1}\big )\). 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.

我们介绍了使用Nesterov-Todd搜索方向进行半定型优化的弧搜索不可行内点算法。该算法基于中心路径的负无穷邻域。该算法沿着整个中心路径的椭圆近似搜索问题的ε近似解。给出了算法的收敛性分析，表明该算法具有迭代复杂度界\（\ mathcal {O} \ big（n ^ {3/2} \ log {\ varepsilon} ^ {-1} \ big）\ ）。在此，n是问题的维数，ε是所需的精度。数值结果表明，该算法是有效且有前途的。