PEPit.primitive_steps.proximal_step
- PEPit.primitive_steps.proximal_step(x0, f, gamma)[source]
This routine performs a proximal step of step-size gamma, starting from x0, and on function f. That is, it performs:
\begin{eqnarray} x \triangleq \text{prox}_{\gamma f}(x_0) & \triangleq & \arg\min_x \left\{ \gamma f(x) + \frac{1}{2} \|x - x_0\|^2 \right\}, \\ & \Updownarrow & \\ 0 & = & \gamma g_x + x - x_0 \text{ for some } g_x\in\partial f(x),\\ & \Updownarrow & \\ x & = & x_0 - \gamma g_x \text{ for some } g_x\in\partial f(x). \end{eqnarray}