A locally smoothing method for mathematical programs with complementarity constraints

Yu Chen, Zhong Wan

Abstract


We propose a locally smoothing method for some mathematical programs with complementarity constraints, which only incurs a local perturbation on these constraints. For the approximate problem obtained from the smoothing method, we show that the Mangasarian–Fromovitz constraints qualification holds under certain conditions. We also analyse the convergence behaviour of the smoothing method, and present some sufficient conditions such that an accumulation point of a sequence of stationary points for the approximate problems is a C-stationary point, an M-stationary point or a strongly stationary point. Numerical experiments are employed to test the performance of the algorithm developed. The results obtained demonstrate that our algorithm is much more promising than the similar ones in the literature.

doi:10.1017/S1446181115000048

Keywords


mathematical programs with complementarity constraints; constraints qualification; convergence; stationary point



DOI: http://dx.doi.org/10.21914/anziamj.v56i0.8170



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.