Thursday, December 21, 2017

Christmas 2017

Sales and support will be closed on 25,26 December and 1 January.

We wish everyone good holiday.
The Christmas trees were created using logistic regression with different levels of regularization. Our implementation used the exponential cone which will be introduced in MOSEK version 9, to be released in 2018. Stay tuned!

Wednesday, December 6, 2017

Workshop: Mixed-integer conic optimization

We are pleased to announce a MOSEK workshop on Mixed-integer conic optimization taking place on Thursday, January 11th, 2018 at our place in the Symbion research park, Copenhagen.

The workshop is free and open to everyone. There will be coffee, refreshments and time for discussions. Please register through this form to help us with planning.

14:00 - 14:05   Welcome (Erling Andersen)
14:05 - 14:50   Tristan Gally
15:00 - 15:45   Julio C. Góez
16:00 - 16:45   Joachim Dahl
17:30+ optional dinner (Nørrebro Bryghus)

  • Tristan Gally, TU Darmstadt, Applications and Solution Approaches for Mixed-Integer Semidefinite ProgrammingMixed-integer semidefinite programming (MISDP) has received increasing attention in recent years. MISDPs appear in many applications either by adding combinatorial decisions to nonlinear problems with natural SDP-formulations or by reformulating combinatorial optimization problems to incorporate stronger SDP-relaxations. While mixed-integer second-order cone programming has been adapted by many commercial solvers, MISDP remains a challenging problem, which so far has mostly been tackled by solution-specific approaches.

    In this talk, we want to present some interesting applications for MISDP from both combinatorial and nonlinear optimization. Afterwards, we will discuss problem-independent solution approaches, mainly concentrating on nonlinear branch-and-bound. Particularly, we will explain the importance of the Slater constraint qualification and its implications for using interior-point methods within a branch-and-bound approach. We will further discuss enhancing techniques like dual fixing and warmstarts and give numerical results comparing the different solution approaches and different implementations.
  • Julio C. Góez, NHH, Disjunctive conic cuts: the good, the bad, and implementation In recent years, the generalization of Balas disjunctive cuts for mixed integer linear optimization problems to mixed integer non-linear optimization problems has received significant attention. Among these studies, mixed integer second order cone optimization (MISOCO) is a special case. For MISOCO one has the disjunctive conic cuts approach. That generalization introduced the concept of disjunctive conic cuts (DCCs) and disjunctive cylindrical cuts (DCyCs). Specifically, it showed that under some mild assumptions the intersection of those DCCs and DCyCs with a closed convex set, given as the intersection of a second order cone and an affine set, is the convex hull of the intersection of the same set with a parallel linear disjunction. The key element in that analysis was the use of pencils of quadrics to find close forms for deriving the DCCs and DCyCs. The first part of this talk will summarize the main results about DCCs and DCyCs including some results about valid conic inequalities for hyperboloids and non-convex quadratic cones when the disjunction is defined by parallel hyperplanes. In the second part, we will discussed some of the limitation of this approach to derive useful valid inequalities in the context of MISOCO. In the last part, we will briefly describe the software libraries that together constitute DisCO, a full-featured solver for MISOCP which we are currently used to explore the potential of DCCs and DCyCs.
  • Joachim Dahl, MOSEK, Mixed-integer conic optimization using MOSEK
    Recently Lubin showed that all the convex instances of the nonlinear mixed-integer bench library MINLPLIB2 can be reformulated as conic optimization problems using 5 different cone types which are the linear, the quadratic, the semidefinite, the exponential and the power cones. The former three cones belong to the class of symmetric cones whereas the latter two belong to the class of nonsymmetric cones. We call modelling with affine expressions and the five previously mentioned cone types extreme desciplined modelling. Based on Lubin et al. and the experience at our company we claim almost all practical convex optimization can be expressed using extreme disciplined modelling so it is a general framework. Now it is much easier to build optimization algorithms and software for extreme disciplined optimization models rather than for general convex (unstructured) convex problems because of limited and explicit structure. This fact is exploited in the software package MOSEK to be discussed. The software package MOSEK has for many years been able to solve conic optimization over the symmetric cones but in the upcoming version 9 MOSEK can also handle two nonsymmetric cones i.e. the exponential and the power cone. In this presentation we will discuss the continuous and mixed-integer conic optimizer in MOSEK. In addition extensive computational results are presented that illustrate the performance of MOSEK on problems including nonsymmetric cones.

Thursday, November 9, 2017

Update in MOSEK Python implementation

All users of MOSEK version 8.1 from Python (especially Python Fusion API) are recommended to upgrade to version for efficiency reasons.

Monday, October 23, 2017

Machine learning in Julia Meetup

On Monday, November 20, 2017 we are hosting a meetup organized by JuliaCPH with the topic of Machine Learning in Julia. Enthusiasts of Julia, machine learning and optimization are welcome! For details see

Tuesday, August 22, 2017

MOSEK 8.1 is out

We are releasing MOSEK 8.1, an improved continuation of version 8.0.

Its main features are:
  • Much faster implementation of the Python Fusion API. Depending on the use case the overhead of Fusion is reduced by a factor of 3-10 on large models.
  • Introduced C++ Fusion API for 64bit Windows, at least for Microsoft Visual Studio 2015+.
  • Performance improvements in the conic optimizer and presolve. Particularly for problems with many dense columns.
  • Improved documentation for the Optimizer, Fusion and API reference. 
All interfaces are identical to that of 8.0, meaning a seamless update.

Platform support changes:
  • Introduced C++ Fusion for 64bit Windows.
  • Dropped support for Python 3.4.
  • Dropped the AMPL shell in 32bit Windows.
Quick links:

Friday, June 30, 2017

MOSEK 8.1 beta

We are releasing a beta version of MOSEK 8.1. It is available for download from a separate page

We expect it to replace the main branch 8.0 after a few months of testing. 

The API of version 8.1 is identical with 8.0, but there are other major upgrades:

  • Much faster implementation of the Python Fusion API. Depending on the use case the overhead of Fusion is reduced by a factor of 3-10 on large models.
  • C++ Fusion API is now available also for Windows, at least for Microsoft Visual Studio 2015 and newer. (Currently only 64bit; the 32bit version is in preparation)
  • Some performance improvements in the conic optimizer. Particularly for problems with many dense columns.
  • Much improved documentation for the Optimizer, Fusion and API reference. 

Thursday, May 11, 2017

Biggest conic quadratic problem solved by MOSEK ever

Recently we got a bug report from a customer. The reason for the bug was that the problem has more than 2^31 nonzeros in the A matrix so a 32 bit integer overflow triggered an assert.

After fixing the bug the problem was not solvable on the largest computer which we had access to. After buying a new DELL PowerEdge R730 server with 2 Xeon E5-2687W v4 3.0GHZ  and 512GB the problem solved in about 2000 seconds using 24 threads using the latest MOSEK version

Here are the size details about the problem:

  • Number linear constraints: 140623
  • Number of variables: 545634
  • Number conic constraints: 124801
  • Number of nonzeros in A: 2208749451 (>2^31)
  • Number of flops per iteration: 10^13

Because the bug discussed above is present in all previous versions of MOSEK then this is the biggest problem in terms of A nonzeros solved by MOSEK ever.

Tuesday, April 4, 2017

Easter holidays 2017

Our support and sales will be closed for Easter holidays from and including Thursday, April 13th until and including Monday, April 17th. We resume on Tuesday, April 18th.

Wishing everyone a good Easter,
The MOSEK team

DTU Power Systems and Electricity Markets School 2017

On June 12-16 the The Energy Analytics and Markets Group at the Technical University of Denmark (DTU) is hosting a Summer School Modern Challenges in Power System Operation and Electricity Markets: An Optimization Perspective. This is the second DTU summer school on the topic of electricity markets and power systems, and as before it will have outstanding speakers.

We are very happy to be one of the sponsors of the school. In particular, two MOSEK scholarships are waiting for two outstanding student participants.

Registration is open until May 7th. We hope to see you at the school in June!

Friday, March 3, 2017

Power flow problems - workshop summary

On February 28th we held the Workshop on Semidefinite Optimization in Power Flow problems.

  • Spyros Chatzivasileiadis gave a talk about SDO methods for producing stability certificates for power systems and about the optimal power flow under uncertainty.
  • Cédric Josz introduced the complex variant of the Lasserre moment hierarchy and discussed the possible advantages of a convex optimizer working directly over the complex numbers.
  • Martin Skovgaard Andersen talked about numerical aspects and experiments with convex relaxations of optimal flow problems. In particular, he was able to solve the SDP relaxations of test cases with over 10K power buses using MOSEK.

The slides from all three talks can be found on our website.

We thank the speakers and the participants for making this a great workshop!


Friday, February 24, 2017

Sponsorship: NemFest, Atlanta, 11-12 May 2017

We are very proud to be one of the sponsors of NemFest 2017 taking place May 11-12, 2017 in Atlanta.

NemFest 2017 is a conference in honor of two extraordinary researchers who shaped the area of discrete and comtinuous optimization: George Nemhauser and Arkadi Nemirovski.

Arkadi Nemirovski was one of the first users of MOSEK back in 1998, even before the release of the first official version.


Tuesday, February 21, 2017

Sponsorship: MIP 2017 - Montréal, 19-22 June

MOSEK is once again one of the sponsors of the Mixed Integer Programming Workshop, which will take place June 19-22, 2017 at HEC Montréal (Québec, Canada).

The program includes talks from distinguished specialists from the academic and industrial world. Until March 1st you can still submit a poster abstract and apply for travel support for students and postdocs.

More details on the official workshop website.


Tuesday, January 3, 2017

Semidefinite optimization in power flow problems

We are pleased to announce a MOSEK workshop on Semidefinite optimization in power flow problems taking place on Tuesday, February 28th, 2017 at the Symbion research park.

Optimal power flow is one of the major problems in optimization of electric power systems, asking for the minimization of operating costs in terms of a specified objective function in the presence of non-linear power flow equations. Three experts, Spyros Chatzivasileiadis (DTU), Cédric Josz (CNRS) and Martin Skovgaard Andersen (DTU) will discuss recent advanced based on convex relaxations and in particular on semidefinite programming.

The workshop is free and open to everyone. There will be coffee, refreshments and time for discussions. Please register through this form to help us with planning.

14:00 - 14:05   Welcome
14:05 - 14:50   Spyros Chatzivasileiadis
15:00 - 15:45   Cédric Josz
16:00 - 16:45   Martin Skovgaard Andersen
17:30+ optional dinner (Nørrebro Bryghus)

  • Spyros Chatzivasileiadis, DTU
    SDP Problems for Power System Stability and Optimization
    In recent years, semidefinite programming is met with increasing interest within the power systems community. Its most notable application to-date is on the convex formulation of the AC optimal power flow problem. At the same time, semidefinite programs can be used to derive Lyapunov functions that guarantee power system stability.

    In this talk we will report on recent work both on power system stability and optimization. First, we will present a novel robust stability toolbox for power grids that can address uncertainties in equilibrium points and fault-on dynamics. In that, we bring in the quadratic Lyapunov functions approach to transient stability assessment.

    Second, we will propose formulations for the integration of chance constraints for several uncertain variables in the optimal power flow problem. We demonstrate our method with numerical examples, and we investigate the conditions to achieve zero duality gap.
  • Cédric Josz, LAAS CNRS
    Application of Polynomial Optimization to Electricity Transmission Networks
    Multivariate polynomial optimization where variables and data are complex numbers is a non-deterministic polynomial-time hard problem that arises in various applications such as electric power systems, imaging science, signal processing, and quantum mechanics. We transpose to complex numbers the Lasserre hierarchy which aims to solve real polynomial optimization problems to global optimality. This brings complex semidefinite programming into the picture and calls for an interior-point algorithm in complex numbers. The Nesterov-Todd direction will be discussed and supplemented by numerical results on the European high-voltage electricity transmission network.
  • Martin Skovgaard Andersen, DTU
    Numerical Aspects of Semidefinite Relaxations of Optimal Power Flow Problems
    Power flow optimization plays an important role in power system operation and planning. It is used to find a cost-optimal operating point of a power system that consists of a set of power buses that are interconnected through a network of transmission lines. We discuss recent progress based on convex relaxation techniques for optimal power flow problems and investigate some numerical aspects through an empirical study.