A Smoothing SQP Method for Mathematical Programs with Linear Second-Order Cone Complementarity Constraints

A Smoothing SQP Method for Mathematical Programs with Linear Second-Order Cone Complementarity Constraints. Yamamura, H., Okuno, T., Hayashi, S., & Fukushima, M.
abstract bibtex

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 P0 property and the nondegeneracy assumptions. We ﬁnally observe the eﬀectiveness of the algorithm by means of numerical experiments.

@article{yamamura_smoothing_nodate,
	title = {A {Smoothing} {SQP} {Method} for {Mathematical} {Programs} with {Linear} {Second}-{Order} {Cone} {Complementarity} {Constraints}},
	abstract = {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 P0 property and the nondegeneracy assumptions. We ﬁnally observe the eﬀectiveness of the algorithm by means of numerical experiments.},
	language = {en},
	author = {Yamamura, Hiroshi and Okuno, Takayuki and Hayashi, Shunsuke and Fukushima, Masao},
	keywords = {/unread, ⛔ No DOI found},
}

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