A General Self-Adaptive Relaxed-PPA Method for Convex Programming with Linear Constraints

Abstract EN

We present an efficient method for solving linearly constrained convex programming.

Our algorithmic framework employs an implementable proximal step by a slight relaxation to the subproblem of proximal point algorithm (PPA).

In particular, the stepsize choice condition of our algorithm is weaker than some elegant PPA-type methods.

This condition is flexible and effective.

Self-adaptive strategies are proposed to improve the convergence in practice.

We theoretically show under mild conditions that our method converges in a global sense.

Finally, we discuss applications and perform numerical experiments which confirm the efficiency of the proposed method.

Comparisons of our method with some state-of-the-art algorithms are also provided.