A corrector–predictor path-following algorithm for semidefinite optimization

A corrector–predictor algorithm is proposed for solving semidefinite optimization problems. In each two steps, the algorithm uses the Nesterov–Todd directions. The algorithm produces a sequence of iterates in a neighborhood of the central path based on a new proximity measure. The predictor step uses line search schemes requiring the reduction of the duality gap, while the corrector step is used to restore the iterates to the neighborhood of the central path. Finally, the algorithm has [Formula: see text] iteration complexity.

A predictor-corrector path-following algorithm for symmetric optimization based on Darvay's technique

In this paper, we present a predictor-corrector path-following interior-point algorithm for symmetric cone optimization based on Darvay's technique. Each iteration of the algorithm contains a predictor step and a corrector step based on a modification of the Nesterov and Todd directions. Moreover, we show that the algorithm is well defined and that the obtained iteration bound is o(?rlogr?/?), where r is the rank of Euclidean Jordan algebra.

PREDICTOR-CORRECTOR DOMAIN DECOMPOSITION ALGORITHM FOR PARABOLIC PROBLEMS ON GRAPHS

In this paper, we present a predictor-corrector type algorithm for solution of linear parabolic problems on graph structure. The graph decomposition is done by dividing some edges and therefore we get a set of problems on sub-graphs, which can be solved efficiently in parallel. The convergence analysis is done by using the energy estimates. It is proved that the proposed finite-difference scheme is unconditionally stable but the predictor step error gives only conditional approximation. In the second part of the paper it is shown that the presented algorithm can be written as Douglas type scheme, based on the domain decomposition method. For a simple case of one dimensional parabolic problem, the convergence analysis is done by using results from [P. Vabishchevich. A substracturing domain decomposition scheme for unsteady problems. Comp. Meth. Appl. Math. 11(2):241-268, 2011]. The optimality of asymptotical error estimates is investigated. Results of computational experiments are presented.