Geodesic
A new one-step smoothing newton method for second-order cone programming
Applications of Mathematics, Tome 57 (2012) no. 4, pp. 311-331.

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In this paper, we present a new one-step smoothing Newton method for solving the second-order cone programming (SOCP). Based on a new smoothing function of the well-known Fischer-Burmeister function, the SOCP is approximated by a family of parameterized smooth equations. Our algorithm solves only one system of linear equations and performs only one Armijo-type line search at each iteration. It can start from an arbitrary initial point and does not require the iterative points to be in the sets of strictly feasible solutions. Without requiring strict complementarity at the SOCP solution, the proposed algorithm is shown to be globally and locally quadratically convergent under suitable assumptions. Numerical experiments demonstrate the feasibility and efficiency of our algorithm.
DOI : 10.1007/s10492-012-0019-6
Classification : 49M15, 49M37, 65K05, 65Y20, 90C25, 90C30, 90C46, 90C53
Keywords: second-order cone programming; smoothing Newton method; global convergence; quadratic convergence; Fischer-Burmeister function; Euclidean Jordan algebra; local quadratic convergence 
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     title = {A new one-step smoothing newton method for second-order cone programming},
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Tang, Jingyong; He, Guoping; Dong, Li; Fang, Liang. A new one-step smoothing newton method for second-order cone programming. Applications of Mathematics, Tome 57 (2012) no. 4, pp. 311-331. doi : 10.1007/s10492-012-0019-6. http://geodesic.mathdoc.fr/articles/10.1007/s10492-012-0019-6/

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