Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1169.49031
Pan, Shaohua; Chen, Jein-Shan
A damped Gauss-Newton method for the second-order cone complementarity problem.
(English)
[J] Appl. Math. Optim. 59, No. 3, 293-318 (2009). ISSN 0095-4616; ISSN 1432-0606/e

Summary: We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem as a semismooth system of equations. Specifically, we characterize the $B$-subdifferential of the FB function at a general point and study the condition for every element of the $B$-subdifferential at a solution being nonsingular. In addition, for the induced FB merit function, we establish its coerciveness and provide a weaker condition than {\it J.-S. Chen} and {\it P. Tseng} [Math. Program. 104, No. 2--3 (B), 293--327 (2005; Zbl 1093.90063)] for each stationary point to be a solution, under suitable Cartesian $P$-properties of the involved mapping. By this, a damped Gauss-Newton method is proposed, and global and superlinear convergence results are obtained. Numerical results are reported for the second-order cone programs from the DIMACS library, which verify the good theoretical properties of the method.
MSC 2000:
*49M15 Methods of Newton-Raphson, Galerkin and Ritz types
49J52 Nonsmooth analysis (other weak concepts of optimality)
90C33 Complementarity problems

Keywords: second-order cones; complementarity; Fischer-Burmeister function; $B$-subdifferential; generalized Newton method

Citations: Zbl 1093.90063

Highlights
Master Server