A Three-Operator Splitting Scheme and its Optimization Applications

Understand

Operator splitting schemes have been successfully used in computational sciences to reduce complex problems into a series of simpler subproblems.

• Since 1950s, these schemes have been widely used to solve problems in PDE and control.
• Recently, large-scale optimization problems in machine learning, signal processing, and imaging have created a resurgence of interest in operator-splitting based algorithms because they often have simple descriptions, are easy to code, and have (nearly) state-of-the-art performance for large-scale optimization problems.
• Although operator splitting techniques were introduced over 60 years ago, their importance has significantly increased in the past decade.