How to set lambda_k of proximal point algorithm?
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The regularization parameter λ_k in the proximal point algorithm can be set such that it satisfies certain conditions. If λ_k satisfies a condition of the form λ_k > 0 and λ_k ≤ 1/η, where η is a positive constant, then the sequence generated by the algorithm is well-defined and converges to a stationary point . Additionally, if λ_k satisfies an additional condition of the form λ_k ≤ 1/L, where L is a positive constant, then the algorithm converges to an optimal solution . The convergence of the proximal point algorithm is also guaranteed when λ_k satisfies a relaxed restriction of the form supK>0 ηKη1 . Different techniques and conditions have been proposed for setting λ_k in the proximal point algorithm, with varying restrictions on the sequence η_k .
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