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A non-interior continuation method for second-order cone programming. (English) Zbl 1177.90318
Summary: We extend the smoothing function proposed by Z. H. Huang, J. Han and Z. Chen [J. Optimization Theory Appl. 117, No. 1, 39–68 (2003; Zbl 1044.90081)] for the non-linear complementarity problems to the second-order cone programming (SOCP). Based on this smoothing function, a non-interior continuation method is presented for solving the SOCP. The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that our algorithm is globally and locally superlinearly convergent in absence of strict complementarity at the optimal solution. Numerical results indicate the effectiveness of the algorithm.

MSC:
90C25 Convex programming
90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
Citations:
Zbl 1044.90081
Software:
SDPT3
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References:
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