Abstract

We show that the Mordukhovich-stationarity system associated with a mathematical program with complementarity constraints (MPCC) can be equivalently written as a system of discontinuous equations which can be tackled with a semismooth Newton method. It will be demonstrated that the resulting algorithm can be interpreted as an active set strategy for MPCCs. Local fast convergence of the method is guaranteed under validity of an MPCC-tailored version of LICQ and a suitable strong second-order condition. In case of linear-quadratic MPCCs, the LICQ-type constraint qualification can be replaced by a weaker condition which depends on the underlying multipliers. We discuss a suitable globalization strategy for our method. Some numerical results are presented in order to illustrate our theoretical findings.

Keywords

  1. active set method
  2. mathematical program with complementarity constraints
  3. M-stationarity
  4. nonlinear M-stationarity function
  5. semismooth Newton method

MSC codes

  1. 49M05
  2. 49M15
  3. 90C30
  4. 90C33

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Information & Authors

Information

Published In

cover image SIAM Journal on Optimization
SIAM Journal on Optimization
Pages: 1459 - 1488
ISSN (online): 1095-7189

History

Submitted: 24 February 2020
Accepted: 16 February 2021
Published online: 27 May 2021

Keywords

  1. active set method
  2. mathematical program with complementarity constraints
  3. M-stationarity
  4. nonlinear M-stationarity function
  5. semismooth Newton method

MSC codes

  1. 49M05
  2. 49M15
  3. 90C30
  4. 90C33

Authors

Affiliations

Funding Information

Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659 : WA 3636/4-2

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