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Volume 3, Issue 3
Superlinear Convergence of a Smooth Approximation Method for Mathematical Programs with Nonlinear Complementarity Constraints

Fujian Duan & Lin Fan

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 367-386.

Published online: 2010-03

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  • Abstract

Mathematical programs with complementarity constraints (MPCC) is an important subclass of MPEC. It is a natural way to solve MPCC by constructing a suitable approximation of the primal problem. In this paper, we propose a new smoothing method for MPCC by using the aggregation technique. A new SQP algorithm for solving the MPCC problem is presented. At each iteration, the master direction is computed by solving a quadratic program, and the revised direction for avoiding the Maratos effect is generated by an explicit formula. As the non-degeneracy condition holds and the smoothing parameter tends to zero, the proposed SQP algorithm converges globally to an S-stationary point of the MPEC problem, its convergence rate is superlinear. Some preliminary numerical results are reported.

  • Keywords

Mathematical programs with complementarity constraints, nonlinear complementarity constraints, aggregation technique, S-stationary point, global convergence, super-linear convergence.

  • AMS Subject Headings

90C30, 65K05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-3-367, author = {}, title = {Superlinear Convergence of a Smooth Approximation Method for Mathematical Programs with Nonlinear Complementarity Constraints}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {3}, pages = {367--386}, abstract = {

Mathematical programs with complementarity constraints (MPCC) is an important subclass of MPEC. It is a natural way to solve MPCC by constructing a suitable approximation of the primal problem. In this paper, we propose a new smoothing method for MPCC by using the aggregation technique. A new SQP algorithm for solving the MPCC problem is presented. At each iteration, the master direction is computed by solving a quadratic program, and the revised direction for avoiding the Maratos effect is generated by an explicit formula. As the non-degeneracy condition holds and the smoothing parameter tends to zero, the proposed SQP algorithm converges globally to an S-stationary point of the MPEC problem, its convergence rate is superlinear. Some preliminary numerical results are reported.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2010.33.6}, url = {http://global-sci.org/intro/article_detail/nmtma/6004.html} }
TY - JOUR T1 - Superlinear Convergence of a Smooth Approximation Method for Mathematical Programs with Nonlinear Complementarity Constraints JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 367 EP - 386 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2010.33.6 UR - https://global-sci.org/intro/article_detail/nmtma/6004.html KW - Mathematical programs with complementarity constraints, nonlinear complementarity constraints, aggregation technique, S-stationary point, global convergence, super-linear convergence. AB -

Mathematical programs with complementarity constraints (MPCC) is an important subclass of MPEC. It is a natural way to solve MPCC by constructing a suitable approximation of the primal problem. In this paper, we propose a new smoothing method for MPCC by using the aggregation technique. A new SQP algorithm for solving the MPCC problem is presented. At each iteration, the master direction is computed by solving a quadratic program, and the revised direction for avoiding the Maratos effect is generated by an explicit formula. As the non-degeneracy condition holds and the smoothing parameter tends to zero, the proposed SQP algorithm converges globally to an S-stationary point of the MPEC problem, its convergence rate is superlinear. Some preliminary numerical results are reported.

Fujian Duan & Lin Fan. (2020). Superlinear Convergence of a Smooth Approximation Method for Mathematical Programs with Nonlinear Complementarity Constraints. Numerical Mathematics: Theory, Methods and Applications. 3 (3). 367-386. doi:10.4208/nmtma.2010.33.6
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