Mathematical programs with complementarity constraints: convergence properties of a smoothing method

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Bouza Allende, G. and Still, G.J. (2007) Mathematical programs with complementarity constraints: convergence properties of a smoothing method. Mathematics of Operations Research, 32 (2). pp. 467-483. ISSN 0364-765X

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Abstract:In this paper, optimization problems $P$ with complementarity constraints are considered. Characterizations for local minimizers $\bar{x}$ of $P$ of Orders 1 and 2 are presented. We analyze a parametric smoothing approach for solving these programs in which $P$ is replaced by a perturbed problem $P_{\tau}$ depending on a (small) parameter $\tau$. We are interested in the convergence behavior of the feasible set $\cal{F}_{\tau}$ and the convergence of the solutions $\bar{x}_{\tau}$ of $P_{\tau}$ for $\tau\to 0.$ In particular, it is shown that, under generic assumptions, the solutions $\bar{x}_{\tau}$ are unique and converge to a solution $\bar{x}$ of $P$ with a rate $\cal{O}(\sqrt{\tau})$. Moreover, the convergence for the Hausdorff distance $d(\cal{F}_{\tau}$, $\cal{F})$ between the feasible sets of $P_{\tau}$ and $P$ is of order $\cal{O}(\sqrt{\tau})$.

Item Type:Article
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/64357
Official URL:http://dx.doi.org/10.1287/moor.1060.0245
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