Numerical stability and efficiency of penalty algorithms. (English) Zbl 0816.65039

Dussault, Jean-Pierre

SIAM J. Numer. Anal. 32, No. 1, 296-317 (1995).

The author considers a variational inequality problem consisting to find a feasible \(x^*\) for which \(F(x^*)^ t(y - x^*) \geq 0\), \(\forall y \in C\). A sufficient condition to ensure that the problem possesses a solution is to require that \(F\) be monotone and that \(C\) be convex compact. Penalty algorithms are used for solving such problems but numerical instabilities may arise. The author proposes remedies to such problems and presents a wide class of numerically stable penalty algorithms. A family of globally convergent, two step superlinearly convergent, numerically stable algorithms are given and implementation of such algorithms is discussed.

Reviewer: Y.Cherruault (Paris)

MSC:

65K10	Numerical optimization and variational techniques
49M30	Other numerical methods in calculus of variations (MSC2010)
49J40	Variational inequalities

Keywords:

numerical stability; global superlinear convergence; penalty algorithms; variational inequality