## Wednesday, March 11, 2020

### Coronavirus COVID-19

March 11th: As of now Denmark locks down for at least 2 weeks in response to the coronavirus pandemic. In the interest of public health we close the MOSEK physical office and continue working from home. At the moment we don't expect any major disruptions, although small delays in e-mail responses are possible. Thank you in advance for your patience.

March 16th: If you are working from home and for this reason require some special arrangements regarding the license, send us an email to support@mosek.com.

We will update this post if there is important new information.

## Monday, March 9, 2020

### Parametrized Fusion - benchmarks

We present some indicative benchmarks of the new Parametrized Fusion, to be released in MOSEK 9.2. We compare a few typical optimization models being reoptimized in two scenarios:

• the model is constructed from scratch with new data for each optimization, MOSEK version 9.1 (green bars)
• the parametrized model is constructed once and parameters are set before every optimization, MOSEK version 9.2 (blue bars)
The red bar in all cases represents the amount of time spent in the optimizer.

## 1. Markowitz portfolio optimization

Here we consider a simple model
$$\begin{array}{ll}\mbox{maximize} & \mu^T x \\ \mbox{subject to} & e^Tx=1,\\ & \gamma \geq \|Fx\|_2, \\ & x\geq 0, \end{array}$$

where
• $x\in\mathbb{R}^{2000}$,
• $F\in \mathbb{R}^{200\times 2000}$ is a dense matrix,
• $\gamma$ is the only parameter changed between optimizations,
• we resolve the model for 200 values of $\gamma$.
Note that by parametrizing we avoid inputting the same big matrix $F$ over and over again.

## 2. Various models

Next we run a few models implemented in Python only.
• MPC - Model Predictive Control similar as in this demo with 15 states, 8 inputs, horizon length $T=80$, parametrized by the initial state, 100 resolves,
• Polytopes - a geometric polytope containment problem, the parameter is a $3\times 3$ matrix $P$ which enters in many constraints of the form $Px=y$, 1000 resolves.
• Elastic - a linear regression model with main term $\|Ax-b\|_2$, where $A\in\mathbb{R}^{3000\times 100}$ is dense, parametrized by $b\in\mathbb{R}^{3000}$, 60 resolves.
• Option - a big option pricing model with complicated structure and multiple parameters, 10 resolves.

## Tuesday, March 3, 2020

### CVX 2.2 supports exponential cone in MOSEK

New features in CVX!

The last release 2.2 of CVX comes with support for the exponential cone in MOSEK. It means that problems involving log, exp, rel_entr, log_det, kl_div and other variants of logarithms and exponentials will be passed directly to a single MOSEK solve without employing a successive approximation method.

CVX 2.2 also comes bundled with the very recent MOSEK 9.1.9.

For an example of a log_det problem with MOSEK output in CVX 2.2 see:

http://web.cvxr.com/cvx/examples/log_exp/html/sparse_covariance_est.html

(Note, though, that the CVX warning about using the successive approximation method is still displayed, but if your log output consists of a single Mosek solve like above then it can be ignored.)