TY - JOUR
T1 - Superlinear Convergence of a Smooth Approximation Method for Mathematical Programs with Nonlinear Complementarity Constraints
AU - Fujian Duan & Lin Fan
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 - <p style="text-align: justify;">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.</p>