On the convergence of the proximal point algorithm for convex minimization
SIAM Journal on Control and Optimization
Proximal minimization algorithm with D-functions
Journal of Optimization Theory and Applications
Variational Principles and Well-Posedness in Optimization and Calculus of Variations
SIAM Journal on Control and Optimization
Bregman Monotone Optimization Algorithms
SIAM Journal on Control and Optimization
Asymptotic Convergence Analysis of a New Class of Proximal Point Methods
SIAM Journal on Control and Optimization
A Proximal-Projection Method for Finding Zeros of Set-Valued Operators
SIAM Journal on Control and Optimization
The Proximal Average: Basic Theory
SIAM Journal on Optimization
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We study the convergence of a proximal point method in a Hilbert space under the presence of computational errors. Most results known in the literature establish the convergence of proximal point methods when computational errors are summable. In the present paper the convergence of the method is established for nonsummable computational errors. We show that the proximal point method generates a good approximate solution if the sequence of computational errors is bounded from above by some constant.