## Wednesday, January 31, 2018

MOSEK version 9 is scheduled for release in early 2019. In this blog post we will outline some of the expected changes. Please note this is subject to change and hence the blogpost will be updated occasionally.

The major new feature in version 9 is support for exponential cone

$$x\geq y\exp(z/y)$$

and power cone

$$x^\alpha y^{1-\alpha}\geq |z|$$

This has the implication that almost any practical convex optimization problem can be formulated directly on conic form. That includes modeling functions such as $x^\alpha$, $x^{1.5}$, $\log{x}$, $e^x$, relative entropy, $p$-norm, logistic, Kullback–Leibler divergence, Cobb-Douglas etc.

Mixed-integer optimization will be available for all conic problems without semi-definite matrix variables. Hence, version 9 should be able to handle almost all mixed-integer optimization problems appearing in practice.

An advantage of moving to the conic form is that it become possible for MOSEK to solve the dual problem if deemed worthwhile. This sometimes leads to dramatic speed ups.

The general nonlinear convex optimizer will be dropped, since optimization problems in conic form are preferred for efficiency and stability reasons. Quadratic and quadratically constrained problems remain unaffected.

Below the planned changes are listed in some detail. Please send us an e-mail to support@mosek.com if you have questions or comments.

### Feature changes

• Adding support for the exponential and power cones in all interfaces.
• Adding mixed-integer support for new cone types.
• Dropping support for general convex optimization problems.

### Interface changes

OPTIMIZER API
• Remove SCopt, DGopt, EXPopt which depended on the general nonlinear optimizer.
R
• Remove scopt which depended on the general nonlinear optimizer.
• Add support for conic constraints of the form $Fx+g\in K$.
TOOLBOX FOR MATLAB
• Remove mskenopt, mskscopt and mskgpopt which depended on the general nonlinear optimizer.
• Add support for conic constraints of the form $Fx+g\in K$.
FUSION
• Fusion for MATLAB will be dropped due to technical issues and low demand.
• Improved performance.

### Other changes

• Vastly improved performance on the AMD Ryzen family of CPUs.
• New version of the Modeling Cookbook adapted to new conic features.
• Dropped support reading and writing XML formatted files.
• Dropped near-optimal, near-infeasible and other near- solution statuses.