I am trying to solve some problems that can be mapped in convex optimisation problem.
In particular is for analysis of quantum state tomography data.
In Matlab there are some tools to help you do this, like SeDuMi or CVX
http://sedumi.ie.lehigh.edu
http://cvxr.com/cvx/
But I could not find anything similar in Mathematica, on the web or in the forums.
Does anybody know if there is an easy way of implementing this kind of algorithm in Mathematica?
I would like to avoid to be forced to switch to Matlab to solve this problem. Nothing against it, but I have most of the programming for this state tomography developed in Mathematica.
Thank you very much.
I had also some troubles with Mathematica in
optimization, exactly on convex problems.
I suggest you export to CVX, which will require
some work because it wants the problem in matrix notation.
Otherwise, to remain with the algebraic formulation,
you could try with Maple, which has, as far
as I can tell, better optimizers than Mathematica.
(check the doc to have an idea)
Related
I'm working on a problem that will eventually run in an embedded microcontroller (ESP8266). I need to perform some fairly simple operations on linear equations. I don't need much, but do need to be able work with points and linear equations to:
Define an equations for lines either from two known points, or one
point and a gradient
Calculate a new x,y point on an equation line that is a specific distance from another point on that equation line
Drop a perpendicular onto an equation line from a point
Perform variations of cosine-rule calculations on points and triangle sides defined as equations
I've roughed up some code for this a while ago based on high school "y = mx + c" concepts, but it's flawed (it fails with infinities when lines are vertical), and currently in Scala. Since I suspect I'm reinventing a wheel that's not my primary goal, I'd like to use someone else's work for this!
I've come across CGAL, and it seems very likely it's capable of all this and more, but I have two questions about it (given that it seems to take ages to get enough understanding of this kind of huge library to actually be able to answer simple questions!)
It seems to assert some kind of mathematical perfection in it's calculations, but that's not important to me, and my system will be severely memory constrained. Does it use/offer memory efficient approximations?
Is it possible (and hopefully easy) to separate out just a limited subset of features, or am I going to find the entire library (or even a very large subset) heading into my memory limited machine?
And, I suppose the inevitable follow up: are there more suitable libraries I'm unaware of?
TIA!
The problems that you are mentioning sound fairly simple indeed, so I'm wondering if you really need any library at all. Maybe if you post your original code we could help you fix it--your problem sounds like you need to redo a calculation avoiding a division by zero.
As for your point (2) about separating a limited number of features from CGAL, giving the size and the coding style of that project, from my experience that will be significantly more complicated (if at all possible) than fixing your own code.
In case you want to try a simpler library than CGAL, maybe you could try Boost.Geometry
Regards,
Which of the following optimisation methods can't be done in an optimisation software such as CPLEX? Why not?
Dynamic programming
Integer programming
Combinatorial optimisation
Nonlinear programming
Graph theory
Precedence diagram method
Simulation
Queueing theory
Can anyone point me in the right direction? I didn't find too much information regarding the limitations of CPLEX on the IBM website.
Thank you!
That's kind-of a big shopping list, and most of the things on it are not optimisation methods.
For sure CPLEX does integer programming, non-linear programming (just quadratic, SOCP, and similar but not general non-linear) and combinatoric optimisation out of the box.
It is usually possible to re-cast things like DP as MILP models, but will obviously require a bit of work. Lots of MILP models are also based on graphs, so yes it is certainly possible to solve a lot of graph problems using a MILP solver such as CPLEX.
Looking wider at topics like simulation, then that is quite a different approach. Simulation really is NOT an optimisation method, but it can be used alongside optimisation to get extra insights which may be useful in a business context. Might be used for example to discover some empirical relationships that could be used in an optimisation model by CPLEX.
The same can probably also be said for things like queuing theory, precedence, etc. Basically, use CPLEX as an optimisation tool to solve part or all of your problem once you have structured and analysed it via one of these other approaches.
Hope that helps.
I'm using the minimize function in Z3 a lot and I'm worrying about some scalability issues (when the number of variables I'm minimizing grows). What is the underlying algorithm of "minimize" and is there a general way to speed things up?
See this paper for details on the optimization algorithms used in Z3. Regarding your question about "general way to speed things up:" Impossible to tell without seeing exactly what you're trying to do and how you are encoding it. Posting a concrete example where things don't "scale" might be helpful.
While I am comfortable with optimization problems in Python (and 'R' for that matter) I am curious to know if it can be done in WEKA.
I have X,Y coordinates of several routes and I need to optimize the best overall solution.
Any help would be appreciated...
Weka is a machine learning, not optimization package. While you could try to predict the optimal solution using the machine learning algorithms in Weka, there's nothing to check that a prediction is the optimal solution or even a solution at all.
Definitely sounds to me like you're trying to use the wrong tool for the job.
I have a simple optimization problem and am looking for java software for that.
The Apache math optimization software looks just like what I want but I cant find documentation to suit my needs (where those needs are to useful to a beginner / non maths professional!)
Does anyone know of a worked, simple, example?
In case it helps, the problem is that I want to find the max r where
r1 = s1 * m1
r2 = s2 * m2
and there are some constraints and formula for defining the relationship between the variables. The Excel Solver works fine for this problem. I got LPSolve working great, but this problem requires a multiplication of s and m, so I understand LPSolve cant help as this makes the problem non linear.
I recently ported the derivative-free non-linear constrained optimization code COBYLA2 to Java. Since it does not explicitly rely on derivatives, the algorithm may require quite a few iterations for larger problems. Nonetheless, you are able to formulate your problem with both a non-linear objective function and (potentially) non-linear constraints.
You can read more about it and download the source code from here.
I am not aware of a simple Java-based NLP solver. (I did find an example of Quadratic programming (QP) in Apache Math Works, but it doesn't qualify since you asked for a non-math professional example.)
I have two suggestions for you to solve your non-linear program:
1.. Excel's Solver does have the ability to tackle non-linear problems. (Don't use LPSOLVE.) In fact, NLP is the default mode in Solver.
Here are two links to using Excel to solve NLPs: Example 1 - Step by step Solver walk-through that covers NLP and
Example 2 - A General Neural network example in Excel
Also for Excel, I like Paul Jensen's (utexas) ORMM Add-in's.
He has a module called Teach NLP. Chapter 10 of his book deals with NLP and is available from his site.
2.. If you are going to be doing even some amount of data analysis, then I recommend investing a few hours to download and learn the basics of R.
R has numerous packages and libraries for optimization. optim() and nlme are relavant for solving non-linear programs.
Just for completeness, I mention SAS, MATLAB and CPLEX as other options. If you have access to any of these, they all do a very good job with solving non-linear programs.
Hope these pointers help.