A full-Newton step infeasible-interior-point algorithm for linear complementarity problems

Infeasible Interior-Point Methods for Linear Optimization Based on Large Neighborhood

“…A future research may focus on some new analysis of the algorithm which yields some larger value of θ . -Roos' full-Newton step IIPM was extended to semidefinite optimization (SDO) by Mansouri and Roos [23], to symmetric optimization (SO) by Gu et al [24] and to LCP by Mansouri et al [25]. An extension of large-update FIPMs based on kernel functions to SDO was presented by El Ghami [10].…”

An Adaptive Primal-Dual Full-Newton Step Infeasible Interior-Point Algorithm for Linear Optimization

“…To get iterates that are feasible for (P ν + ) and (D ν + ), we need search directions ∆x and ∆s such that x + ∆x, y + ∆y and s + ∆s satisfy (7). Since x and (y, s) are feasible for (P ν ) and (D ν ), respectively, it follows that ∆x, ∆y and ∆s should satisfy In this paper, we also replace µ at the right hand side of the third equation with µ + := (1 − θ)µ and consider the system…”

“…After accomplishing a few centering steps for the new perturbed problem, it obtains strictly feasible iterates close enough to central path of the new perturbed problems. This algorithm have extensively extended to other optimization problems, e.g., [2,7,[11][12][13]. Subsequently, some authors have tried to improve the Roos's infeasible algorithm, see for example [4,5].…”

An Improved and Simplified Full-Newton Step $O(n)$ Infeasible Interior-Point Method for Linear Optimization

“…See, e.g., [1,3,5,6,7,8,9,12,14]. Many of these methods start with a strictly feasible solution of an artificially constructed problem, and they generate iterates each of which is strictly feasible for that or another artificial problem.…”