Envelope Functions: Unifications and Further Properties
Research output: Contribution to journal › Article
Forward–backward and Douglas–Rachford splitting are methods for structured nonsmooth optimization. With the aim to use smooth optimization techniques for nonsmooth problems, the forward–backward and Douglas–Rachford envelopes where recently proposed. Under specific problem assumptions, these envelope functions have favorable smoothness and convexity properties and their stationary points coincide with the fixed-points of the underlying algorithm operators. This allows for solving such nonsmooth optimization problems by minimizing the corresponding smooth convex envelope function. In this paper, we present a general envelope function that unifies and generalizes existing ones. We provide properties of the general envelope function that sharpen corresponding known results for the special cases. We also present a new interpretation of the underlying methods as being majorization–minimization algorithms applied to their respective envelope functions.
|Research areas and keywords||
Subject classification (UKÄ) – MANDATORY
|Journal||Journal of Optimization Theory and Applications|
|Early online date||2018 Jun 12|
|Publication status||Published - 2018|