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Corrector-predictor methods for sufficient linear complementarity problems

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Abstract

We present a new corrector-predictor method for solving sufficient linear complementarity problems for which a sufficiently centered feasible starting point is available. In contrast with its predictor-corrector counterpart proposed by Miao, the method does not depend on the handicap κ of the problem. The method has \(O((1+\kappa)\sqrt{n}L)\) -iteration complexity, the same as Miao’s method, but our error estimates are sightly better. The algorithm is quadratically convergent for problems having a strictly complementary solution. We also present a family of infeasible higher order corrector-predictor methods that are superlinearly convergent even in the absence of strict complementarity. The algorithms of this class are globally convergent for general positive starting points. They have \(O((1+\kappa)\sqrt{n}L)\) -iteration complexity for feasible, or “almost feasible”, starting points and O((1+κ)2 nL)-iteration complexity for “sufficiently large” infeasible starting points.

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Authors and Affiliations

  1. Department of Mathematics & Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD, 21250, USA

    Filiz Gurtuna, Cosmin Petra, Florian A. Potra & Adrian Vancea

  2. Department of Mathematics, Western Michigan University, 3319 Everett Tower, Kalamazoo, MI, 49008-5248, USA

    Olena Shevchenko

Authors
  1. Filiz Gurtuna
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  2. Cosmin Petra
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  3. Florian A. Potra
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  4. Olena Shevchenko
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  5. Adrian Vancea
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Correspondence to Florian A. Potra.

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Gurtuna, F., Petra, C., Potra, F.A. et al. Corrector-predictor methods for sufficient linear complementarity problems. Comput Optim Appl 48, 453–485 (2011). https://doi.org/10.1007/s10589-009-9263-4

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  • DOI: https://doi.org/10.1007/s10589-009-9263-4

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