Dual Gradient Method with Partial Regularization for Convex Optimization Problems

Key Points

• This research aims to develop a dual gradient method enhanced by partial regularization for convex optimization problems.
• Introduced a class of dual gradient Uzawa type methods for convex constrained optimization problems.
• Implemented partial regularization in primal variables and additional constraints for dual variables.
• Established convergence under general assumptions.
• Demonstrated stable convergence of the proposed method.
• Convergence guarantees are provided based on more general assumptions than previous methods.