Regularized Barzilai-Borwein method
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This paper is concerned with the introduction of regularization into RBB method for solving some ill-posed optimization problems. The step size generated by the BB method is relatively too long, resulting in a very unstable sequence of iterations and non-monotonicity of the objective function value in some difficult problems. A new step size generated by the RBB method is relatively short and is more effective in its ability to overcome the instability of the BB method in such ill-posed problems. At the same time, fast convergence of the RBB method is maintained by the adjustment of regularization parameters. Numerical examples show the benefits of the RBB method for solving some difficult problems.
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