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A globally convergent matrix-free method for constrained equations and its linear convergence rate. (English) Zbl 1470.65119

Summary: A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak) conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor \(\gamma\) is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.

MSC:

65K10 Numerical optimization and variational techniques
65H10 Numerical computation of solutions to systems of equations
90C30 Nonlinear programming
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