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Semismooth Newton method for the lifted reformulation of mathematical programs with complementarity constraints

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Abstract

We consider a reformulation of mathematical programs with complementarity constraints, where by introducing an artificial variable the constraints are converted into equalities which are once but not twice differentiable. We show that the Lagrange optimality system of such a reformulation is semismooth and BD-regular at the solution under reasonable assumptions. Thus, fast local convergence can be obtained by applying the semismooth Newton method. Moreover, it turns out that the squared residual of the Lagrange system is continuously differentiable (even though the system itself is not), which opens the way for a natural globalization of the local algorithm. Preliminary numerical results are also reported.

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Authors and Affiliations

  1. Uchebniy Korpus 2, VMK Faculty, OR Department, Moscow State University, MSU, Leninskiye Gory, 119991, Moscow, Russia

    A. F. Izmailov & A. L. Pogosyan

  2. IMPA—Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, RJ, 22460-320, Brazil

    M. V. Solodov

Authors
  1. A. F. Izmailov
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  2. A. L. Pogosyan
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  3. M. V. Solodov
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Corresponding author

Correspondence to M. V. Solodov.

Additional information

Research of the first two authors is supported by the Russian Foundation for Basic Research Grant 10-01-00251. The third author is supported in part by CNPq Grants 300513/2008-9 and 471267/2007-4, by PRONEX–Optimization, and by FAPERJ.

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Izmailov, A.F., Pogosyan, A.L. & Solodov, M.V. Semismooth Newton method for the lifted reformulation of mathematical programs with complementarity constraints. Comput Optim Appl 51, 199–221 (2012). https://doi.org/10.1007/s10589-010-9341-7

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