A Three-Operator Splitting Scheme and its Optimization Applications

作者：Davis, Damek; Yin, Wotao^*

来源：Set-Valued and Variational Analysis, 2017, 25(4): 829-858.

DOI：10.1007/s11228-017-0421-z

• Operator splitting
• Three operators
• Fixed point
• Convex optimization
• Monotone inclusion
• Acceleration
• Douglas Rachford
• Forward backward

Operator-splitting methods convert optimization and inclusion problems into fixed-point equations; when applied to convex optimization and monotone inclusion problems, the equations given by operator-splitting methods are often easy to solve by standard techniques. The hard part of this conversion, then, is to design nicely behaved fixed-point equations. In this paper, we design a new, and thus far, the only nicely behaved fixed-point equation for solving monotone inclusions with three operators; the equation employs resolvent and forward operators, one at a time, in succession. We show that our new equation extends the Douglas-Rachford and forward-backward equations; we prove that standard methods for solving the equation converge; and we give two accelerated methods for solving the equation.

• 出版日期2017-12