Abstract
A new smoothing approach was given for solving the mathematical programs with complementarity constraints (MPCC) by using the aggregation technique. As the smoothing parameter tends to zero, if the KKT point sequence generated from the smoothed problems satisfies the second-order necessary condition, then any accumulation point of the sequence is a B-stationary point of MPCC if the linear independence constraint qualification (LICQ) and the upper level strict complementarity (ULSC) condition hold at the limit point. The ULSC condition is weaker than the lower level strict complementarity (LLSC) condition generally used in the literatures. Moreover, the method can be easily extended to the mathematical programs with general vertical complementarity constraints.
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Yin, H., Zhang, J. Global Convergence of a Smooth Approximation Method for Mathematical Programs with Complementarity Constraints. Math Meth Oper Res 64, 255–269 (2006). https://doi.org/10.1007/s00186-006-0076-2
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DOI: https://doi.org/10.1007/s00186-006-0076-2