Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2012-005 (June 14, 2012)

A Smoothing SQP Method for Mathematical Programs with Linear Second-Order Cone Complementarity Constraints
by Hiroshi Yamamura, Takayuki Okuno, Shunsuke Hayashi and Masao Fukushima

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In this paper, we focus on the mathematical program with second-order cone (SOC) complementarity constraints, which contains the well-known mathematical program with nonnegative complementarity constraints as a subclass. For solving such a problem, we propose a smoothing-based sequential quadratic programming (SQP) methods. We first replace the SOC complementarity constraints with equality constraints using the smoothing natural residual function, and apply the SQP method to the smoothed problem with decreasing the smoothing parameter. We show that the proposed algorithm possesses the global convergence property under the Cartesian $P_0$ property and the nondegeneracy assumptions. We finally observe the effectiveness of the algorithm by means of numerical experiments.