SIAM Conference on Optimization (OP23)

MOSEK is proud to be one of the sponsors of the SIAM Conference on Optimization (OP23). SIAM OP23 will be held on May 31 - June 3, 2023, at the Sheraton Grand Seattle | Seattle, Washington, U.S.

More details and registration at https://www.siam.org/conferences/cm/conference/op23

Mosek and AMPL

We are pleased to announce that AMPL Inc has become a reseller of MOSEK.

Moreover, a new AMPL to MOSEK interface was made available in the AMPL/MP open-source library of solver interfaces.

Details can be found on the MOSEK for AMPL page.

Easter 2023

Due to Easter support and sales will be closed from Thursday, April 6th, until Monday, April 10th, both days inclusive.

The MOSEK team wishes everyone a peaceful Easter.

Mosek with AmpliconArchitect

AmpliconArchitect (AA), a Python tool for genomic reconstruction used in cancer biology is in the process of updating that will make it compatible with all versions of MOSEK.

Until recently the tool was dependent on an older MOSEK API which required the use of MOSEK 8, making the installation process a bit more cumbersome, and making AA dependent on the discontinued, less accurate general convex optimizer.

With the new updates installing MOSEK for use with AA will be as simple as "pip install mosek" and one gets easy access to MOSEK upgrades the same way. AA will use MOSEK to solve its optimization tasks with the more accurate, faster conic solver.

We would like to thank Jens Luebeck for guidance and help with the installation, running and testing the new software.

For the time being you can try this new version via Jens' fork of AmpliconArchitect, where the readme file also provides all the necessary details. As always you can get a MOSEK personal academic license for academic use of AA via our website.

Design a heart with DJC

In connection with the approaching Christmas, we are receiving many support questions about the use of mixed-integer conic optimization in the design of the traditional Danish "braided heart" Christmas tree decorations:

Let us demonstrate how this can be done with MOSEK. First, we need to define the heart. A suitable model is given by

$$x^2+(y-p|x|)^2\leq r^2,$$

where $p,r$ are parameters which can be adjusted for different shapes and sizes:

This is not a convex shape, but it can still be modelled in conic form if we employ a mixed-integer model of $|x|$. This can be done using a classical big-M approach or, in MOSEK 10, using a disjunctive constraint (DJC):

$$\begin{array}{l}(x\geq 0 \ \mathrm{AND}\ z=x)\ \mathrm{OR}\ (x\leq 0 \ \mathrm{AND}\ z=-x) \\  x^2+(y-pz)^2\leq r^2\end{array},$$

combining a DJC with a quadratic cone constraint in affine conic (ACC) form.

Having defined the domain, it is time to draw some lines with slope $\pm 45^\circ$ to determine the braided pattern. To do this, we will choose, one at a time, line segments with integer endpoints, say $x=(x_1,x_2)$, $y=(y_1,y_2)$, inside the heart. Such a line segment has the correct slope if

$$x_1-x_2=y_1-y_2\ \mathrm{OR}\ x_1+x_2=y_1+y_2,$$

which, again, is a disjunctive constraint. We will only choose sufficiently long line segments, for example by requiring

$$|x_1-y_1|\geq c$$

for some constant $c$. Here the absolute value can again be modelled in the same mixed-integer fashion as before. We set no objective, so this becomes a feasibility problem, but one could also decide, for instance, to maximize the length of the segment or optimize some other measure of beauty for the design.

Having found one segment, we will construct a new one by adding additional constraints to guarantee that the new segments do not interfere too much with the previous ones. For the sake of simplicity, we will demand that new endpoints do not belong to any line of slope $\pm 45^\circ$ containing the previous endpoints, but one could consider other elimination conditions as well. This iterative procedure is similar to solving the travelling salesman problem by cycle elimination, and it terminates once there is no more place for new segments under all the constraints. The implementation requires us to be able to write the "not equals" condition $x\neq a$, which, assuming we work with integers, can again be cast as a DJC:

$$x\leq a-1 \ \mathrm{OR}\ x\geq a+1.$$

The iterative procedure will construct more and more segments:

To obtain different designs, we can vary the parameters $p,r$. Still, there is enough freedom in the choice of segments that even just varying the random seed ("mioSeed") for the mixed-integer optimizer produces different final solutions for the same choice of $p,r$:

And on this note, we leave you with the Fusion API code below and wish you all the best. (You can also read our last Christmas special from way back in 2018).

MOSEK Team

Christmas 2022

During the Christmas period our sales and support will be closed 23-27 December 2022, inclusive. 

The MOSEK Team

MIP 2023 - 20th Anniversary

MOSEK is proud to be one of the sponsors of MIP 2023 - Mixed Integer Programming workshop. MIP 2023 marks the 20th year of the conference and, as such will be particularly special. It will be held May 22-25, 2023, at the University of Southern California, Los Angeles.

More details at https://www.mixedinteger.org/2023/