A hybrid Josephy-Newton method for solving box constrained variational equality problems via the D-gap function

Ji-Ming Peng (1) , Christian Kanzow (2) , Masao Fukushima (3)

1 Institute of Computational Mathematics and Scientific/Engineering Computing
2 Department of Mathematics - University of Hamburg
3 Kyoto University

A box constrained variational inequality problem can be reformulated as an unconstrained minimization problem through the D-gap function. Some basic properties of the affine variational inequality subproblems in the classical Josephy-Newton method are studied. A hybrid Josephy-Newton method is then proposed for minimizing the D-gap function. Under suitable conditions, the algorithm is shown to be globally convergent and locally quadratically convergent. Some numerical results are also presented.

Mots clés: unconstrained optimization; Newton's method; D-gap function; quadratic convergence; global convergence; variational inequality problem; box constraints

Domaines: Mathématiques [math]; Mécanique des structures [physics.class-ph]

Ji-Ming Peng, Christian Kanzow, Masao Fukushima. A hybrid Josephy-Newton method for solving box constrained variational equality problems via the D-gap function. Optimization Methods and Software, 1999, 10 (5), pp.687-710. ⟨10.1080/10556789908805734⟩. ⟨hal-01975369⟩