# Remote Quadratic Programming 

This example considers a strongly convex  optimization problem 
```{math}
\beta^* \in \argmin_{\norm{\beta}_1 \leq \tau} \sum_{i=1}^{5} f_i(\beta),
```
where each function $f_i$ is a quadratic in $S_{m_i, L_i}$.


The overall composite optimization problem is described using the constants
```{math}
\begin{align*}
m &= \mat{cccccc}{0, 1, -2, 1, 1, 0}\\
L &= \mat{cccccc}{5, 2, 1, 6, 1, \infty}.\\
\end{align*}

```

The Synthesized algorithm to solve this problem must have a block-lower-triangular $\Dcl$ matrix. Synthesis of an algorithm with convergence rate $\rho < 0.7679$ is accomplished by using the code
```{literalinclude} ../../../examples/synthesis/syn_server.m
:linenos: true
:caption: Composite Quadratic Programming
:language: matlab
:lines: 1-16
```


Next, the same optimization  problem must be solved in a remote setting. The network dynamics separating the oracles $\partial f$ include time-delays and channel memory. The following code generates an algorithm with $\rho < 0.9341$ in the networked setting.

```{literalinclude} ../../../examples/synthesis/syn_server_channel.m
:linenos: true
:caption: Composite Quadratic Programming with Network Dynamics
:language: matlab
:lines: 1-44
```