This version is supposed to work on all problems (please, let me know if
this is not so), but is not optimized yet in terms of numerical
stability and performance. Bland's rule is implemented as well, so
algorithm is supposed to allow no cycling. Additional check for multiple
solutions is added (in case of multiple solutions algorithm returns an
appropriate return code of 1 and returns arbitrary optimal solution).
Finally, now we have 5 tests.
Before Thursday we have 4 directions that can be tackled in parallel:
*) Prepare the pull request!
*) Make the code more clear and readable (refactoring)
*) Wrap the core solveLP() procedure in OOP-style interface
*) Test solveLP on non-trivial tests (possibly test against
http://www.coin-or.org/Clp/)
What we have now corresponds to "formal simplex algorithm", described in
Cormen's "Intro to Algorithms". It will work *only* if the initial
problem has (0,0,0,...,0) as feasible solution (consequently, it will
work unpredictably if problem was unfeasible or did not have zero-vector as
feasible solution). Moreover, it might cycle.
TODO (first priority)
1. Implement initialize_simplex() procedure, that shall check for
feasibility and generate initial feasible solution. (in particular, code
should pass all 4 tests implemented at the moment)
2. Implement Bland's rule to avoid cycling.
3. Make the code more clear.
4. Implement several non-trivial tests (??) and check algorithm against
them. Debug if necessary.
TODO (second priority)
1. Concentrate on stability and speed (make difficult tests)
At this point we have a skeleton of a new module (optim) which can
barely compile properly (unlike previous commit). Besides, there is a
first draft of solver and lpsolver (linear optimization solver) in this
commit.
Generic optimization package for openCV project, will be developed
between the June and September of 2013. This work is funded by Google
Summer of Code 2013 project. This project is about
implementing several algorithms, that will find global maxima/minima of a
given function on a given domain subject to a given constraints.
All comments/suggestions are warmly appreciated and to be sent to
alozz1991@gmail.com (please, mention the word "openCV" in topic of
message, for I'm using the spam-filters)
