Extending Mehrotra's Corrector for Linear Programs

A constraint-reduced variant of Mehrotra's predictor-corrector algorithm

Consider linear programs in dual standard form with n constraints and m variables. When typical interior-point algorithms are used for the solution of such problems, updating the iterates, using direct methods for solving the linear systems and assuming a dense constraint matrix A, requires O(nm) operations per iteration. When n ≫ m it is often the case that at each iteration most of the constr...

A quadratically convergent predictor-corrector method for solving linear programs from infeasible starting points

A predictor-corrector method for solving linear programs from infeasible starting points is analyzed. The method is quadratically convergent and can be combined with Ye's finite termination scheme under very general assumptions. If the starting points are large enough then the algorithm has O(nL) iteration complexity. If the ratio between feasibility and optimality at the starting points is sma...

Predictor-Corrector Smoothing Methods for Linear Programs with a More Flexible Update of the Smoothing Parameter

Local convergence of predictor-corrector infeasible-interior-point algorithms for SDPs and SDLCPs

An example of SDPs (semide nite programs) exhibits a substantial di culty in proving the superlinear convergence of a direct extension of the Mizuno-Todd-Ye type predictorcorrector primal-dual interior-point method for LPs (linear programs) to SDPs, and suggests that we need to force the generated sequence to converge to a solution tangentially to the central path (or trajectory). A Mizuno-Todd...

Corrector-predictor arc-search interior-point algorithm for $P_*(kappa)$-LCP acting in a wide neighborhood of the central path

In this paper, we propose an arc-search corrector-predictor interior-point method for solving $P_*(kappa)$-linear complementarity problems. The proposed algorithm searches the optimizers along an ellipse that is an approximation of the central path. The algorithm generates a sequence of iterates in the wide neighborhood of central path introduced by Ai and Zhang. The algorithm does not de...