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This paper proposes an inexact interior-point relaxation method (iIPRM) for LO problems that does not require its iterates to remain strictly positive and employs a sparse preconditioner tailored to the structure of the normal matrix.
This work proposes a multiscale primal-dual interior-point relaxation method (IPRM), which can handle instances whose full formulations contain trillions of transport variables and develops an effective support-identification strategy based on the approximate solutions obtained by IPRM.
A primal--dual interior-point method for nonsymmetric conic optimization based on a conjugate-free scaling matrix obtained from a single-secant BFGS update of the primal barrier Hessian, which attains an iteration bound of $\mathcal{O}(\sqrt{\nu}\log(1/\varepsilon)$ and is competitive with QICS, a specialized solver fo...
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