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.