English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We apply novel inner-iteration preconditioned Krylov subspace methods to theinterior-point algorithm for linear programming (LP). Inner-iterationpreconditioners recently proposed by Morikuni and Hayami enable us to overcomethe severe ill-conditioning of linear equations solved in the final phase ofinterior-point iterations. The Krylov subspace methods do not suffer fromrank-deficiency and therefore no preprocessing is necessary even if rows of theconstraint matrix are not linearly independent. By means of these methods, anew interior-point recurrence is proposed in order to omit one matrix-vectorproduct at each step. Extensive numerical experiments are conducted overdiverse instances of 138 LP problems including the Netlib, QAPLIB, Mittelmannand Atomizer Basis Pursuit collections. The largest problem has 434,580unknowns. It turns out that our implementation is more robust than the standardpublic domain solvers SeDuMi (Self-Dual Minimization), SDPT3 (SemidefiniteProgramming Toh-Todd-T\"ut\"unc\"u) and the LSMR iterative solver in PDCO(Primal-Dual Barrier Method for Convex Objectives) without increasing CPU time.The proposed interior-point method based on iterative solvers succeeds insolving a fairly large number of LP instances from benchmark libraries underthe standard stopping criteria. The work also presents a fairly extensivebenchmark test for several renowned solvers including direct and iterativesolvers.

Implementation of Interior-point Methods for LP based on Krylov Subspace Iterative Solvers with Inner-iteration Preconditioning