Geodesic
Analysis of a non-monotone smoothing-type algorithm for the second-order cone programming
Applications of Mathematics, Tome 60 (2015) no. 1, pp. 35-49 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The smoothing-type algorithm is a powerful tool for solving the second-order cone programming (SOCP), which is in general designed based on a monotone line search. In this paper, we propose a smoothing-type algorithm for solving the SOCP with a non-monotone line search. By using the theory of Euclidean Jordan algebras, we prove that the proposed algorithm is globally and locally quadratically convergent under suitable assumptions. The preliminary numerical results are also reported which indicate that the non-monotone smoothing-type algorithm is promising for solving the SOCP.
The smoothing-type algorithm is a powerful tool for solving the second-order cone programming (SOCP), which is in general designed based on a monotone line search. In this paper, we propose a smoothing-type algorithm for solving the SOCP with a non-monotone line search. By using the theory of Euclidean Jordan algebras, we prove that the proposed algorithm is globally and locally quadratically convergent under suitable assumptions. The preliminary numerical results are also reported which indicate that the non-monotone smoothing-type algorithm is promising for solving the SOCP.
DOI : 10.1007/s10492-015-0084-8
Classification : 17C55, 65K05, 90C25, 90C30
Keywords: second-order cone programming; smoothing Newton algorithm; non-monotone line search; convergence 
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Tang, Jingyong; Dong, Li; Fang, Liang; Sun, Li. Analysis of a non-monotone smoothing-type algorithm for the second-order cone programming. Applications of Mathematics, Tome 60 (2015) no. 1, pp. 35-49. doi: 10.1007/s10492-015-0084-8

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