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Chi, Xiaoni; Wang, Yang; Zhu, Zhibin; Wan, Zhongping

Jacobian consistency of a one-parametric class of smoothing Fischer-Burmeister functions for SOCCP. (English) Zbl 1395.90224

Comput. Appl. Math. 37, No. 1, 439-455 (2018).
Summary: The Jacobian consistency of smoothing functions plays an important role for achieving the rapid convergence of Newton methods or Newton-like methods with an appropriate parameter control. In this paper, we study the properties, derive the computable formula for the Jacobian matrix and prove the Jacobian consistency of a one-parametric class of smoothing Fischer-Burmeister functions for second-order cone complementarity problems proposed by J. Tang et al. [ibid. 33, No. 3, 655–669 (2014; Zbl 1308.90173)]. Then we apply its Jacobian consistency to a smoothing Newton method with the appropriate parameter control presented by X. Chen et al. [Math. Comput. 67, No. 222, 519–540 (1998; Zbl 0894.90143)], and show the global convergence and local quadratic convergence of the algorithm for solving the SOCCP under rather weak assumptions.

Cited in 2 Documents

MSC:

90C30 Nonlinear programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
65K10 Numerical optimization and variational techniques

Keywords:

second-order cone complementarity problem; smoothing Fischer-Burmeister function; Jacobian consistency; smoothing Newton method; quadratic convergence

Citations:

Zbl 1308.90173; Zbl 0894.90143
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Full Text: DOI

References:

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