Friday, May 22, 2015

Nonsymmetric semidefinite optimization problems.

In  semidefinite optimization we optimize over a matrix variable that must be symmetric and positive semidefinite.

Assume we want to relax the assumption about symmetry. Is that an important generalization? The answer is no for the following reason. Since 

   (X+X')/2 is PSD



is PSD. Observe

   X = (X+X')/2+(X-X')/2


  y'( (X-X')/2) y >= 0.

implying X is PSD.

Note  (X-X')'=-(X-X') implying X-X' is skew symmetric.

Hence, any nonsymmetric semidefinite optimization problem can easily be posed as a standard symmetric semidefinite optimization problem.

Wednesday, February 18, 2015

Multi threaded programming

I found the talk: Plain Threads are the GOTO of todays computing by Hartmut Kaiser very interesting because I have been working on improving the multithreaded code in MOSEK recently. And is also thinking how MOSEK should deal with all the cores in the CPUs in the future. I agree with Hartmut something else than plain threads is needed.

Here are some potential replacements:
Previously I have used OpenMP but I really dislike that. In my opinion it is somewhat ugly and you feel the Fortran origins. Recently I have played with Cilk which is very simple.

Checkedthreads seems like a good option if a simple C only tool can do the job. I have plan to try that at MOSEK.

Pfunc seems very powerful and there is ph.d. thesis about its design. The project might be semi-dead though.

Wool also seems very interesting. It is plain C and the author claims the spawn overhead is very low. There is also an older comparison with other task libraries.

Btw I biased towards tools that has no C++ bindings because currently MOSEK is plain C code. Adding a dependency on a C++ runtime library adds headaches.

Some common terminology when working on parallism is