I have been using cvx for doing some experiments with my SDPs. Although it is very easy to use, it is quite slow. I cannot run reasonably large instances in reasonable time. Hence would like someone to point to some faster software.
You can find a list of Semidefinite Programming codes on Hans Mittelmann's Decision Tree for Optimization Software. At least some of the codes are implemented in Matlab (like cvx, right?) or have a Matlab interface.
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Are there any faster and more efficient solvers other than fmincon? I'm using fmincon for a specific problem and I run out of memory for modest sized vector variable. I don't have any supercomputers or cloud computing options at my disposal, either. I know that any alternate solution will still run out of memory but I'm just trying to see where the problem is.
P.S. I don't want a solution that would change the way I'm approaching the actual problem. I know convex optimization is the way to go and I have already done enough work to get up until here.
P.P.S I saw the other question regarding the open source alternatives. That's not what I'm looking for. I'm looking for more efficient ones, if someone faced the same problem adn shifted to a better solver.
Hmmm...
Without further information, I'd guess that fmincon runs out of memory because it needs the Hessian (which, given that your decision variable is 10^4, will be 10^4 x numel(f(x1,x2,x3,....)) large).
It also takes a lot of time to determine the values of the Hessian, because fmincon normally uses finite differences for that if you don't specify derivatives explicitly.
There's a couple of things you can do to speed things up here.
If you know beforehand that there will be a lot of zeros in your Hessian, you can pass sparsity patterns of the Hessian matrix via HessPattern. This saves a lot of memory and computation time.
If it is fairly easy to come up with explicit formulae for the Hessian of your objective function, create a function that computes the Hessian and pass it on to fmincon via the HessFcn option in optimset.
The same holds for the gradients. The GradConstr (for your non-linear constraint functions) and/or GradObj (for your objective function) apply here.
There's probably a few options I forgot here, that could also help you. Just go through all the options in the optimization toolbox' optimset and see if they could help you.
If all this doesn't help, you'll really have to switch optimizers. Given that fmincon is the pride and joy of MATLAB's optimization toolbox, there really isn't anything much better readily available, and you'll have to search elsewhere.
TOMLAB is a very good commercial solution for MATLAB. If you don't mind going to C or C++...There's SNOPT (which is what TOMLAB/SNOPT is based on). And there's a bunch of things you could try in the GSL (although I haven't seen anything quite as advanced as SNOPT in there...).
I don't know on what version of MATLAB you have, but I know for a fact that in R2009b (and possibly also later), fmincon has a few real weaknesses for certain types of problems. I know this very well, because I once lost a very prestigious competition (the GTOC) because of it. Our approach turned out to be exactly the same as that of the winners, except that they had access to SNOPT which made their few-million variable optimization problem converge in a couple of iterations, whereas fmincon could not be brought to converge at all, whatever we tried (and trust me, WE TRIED). To this day I still don't know exactly why this happens, but I verified it myself when I had access to SNOPT. Once, when I have an infinite amount of time, I'll find this out and report this to the MathWorks. But until then...I lost a bit of trust in fmincon :)
Is it possible to use a MATLAB code on Scilab? Is that what is meant when saying that Scilab is a "clone" from MATLAB?
There is a tool to automatically convert Matlab source to Scilab source, it's called M2SCI. A script parses the Matlab source code and replaces Matlab-specific functions by Scilab ones. See the documentation of the mfile2sci function.
Yes you can use MATLAB code on scilab. See these links for more information:
http://help.scilab.org/docs/5.4.0/fr_FR/section_36184e52ee88ad558380be4e92d3de21.html
http://help.scilab.org/docs/5.4.0/en_US/index.html
I would not bet on it. But if your code is simple enough chances are good.
Problems are:
There is encrypted p-code in Matlab that Scilab will not be able to open.
Matlab usually comes with a number of toolboxes that might not be available to you (i think especially Simulink)
last but not least (i don't know about scilab) there usually are minute differences in how functions are implemented.
There are a number of projects out there trying to replicate/replace MATLAB:
Julia language: which has a relatively similar syntax to MATLAB and offers great performance, but still lacks a lot of toolboxes/libraries, as well as not having a GUI like MATLAB. I think this has the brightest future among all MATLAB alternatives.
Python language and its libraries NumPy and matplotlib: which is the most used alternative. I think at this moment the community is a couple of orders of magnitude even bigger than MATLAB. Python is the de facto standard in machine learning and data science at the moment. But still, the syntax and memory concept is a bit far from what people are used to in the MATLAB ecosystem. There are also no equivalent to SIMULINK, although Spyder and Jupyter projects have come a long way in terms of the development environment.
Octave: is basically a clone of MATLAB to a point they consider any incompatibility as a bug. If you have a long MATLAB code that you don't want to touch, this is the safest bet. But again no alternative for SIMULINK.
SciLab and it's fork ScicoLab are the best alternatives in terms of GUI, having a SIMULINK replica xcos / scicos and a graphical user interface development features. However the community is not as big as Octave and the syntax is not completely compatible. Sadly the Scilab development team has gone through a devastating family crisis leading to the software falling behind.
Honorary mention of Modelica language implementations OpenModelica and jModelica for being a superior alternative to SIMULINK-SimScape. You should know that you can load Modelica scrips also in xcos and scicos. If you want to kno wmore about JModelica you may see this post.
you may check the MATLAB's Alternativeto page to see more Free and Open source alternatives.
I have to solve a multiobjective problem but I don't know if I should use CPLEX or Matlab. Can you explain the advantage and disadvantage of both tools.
Thank you very much!
This is really a question about choosing the most suitable modeling approach in the presence of multiple objectives, rather than deciding between CPLEX or MATLAB.
Multi-criteria Decision making is a whole sub-field in itself. Take a look at: http://en.wikipedia.org/wiki/Multi-objective_optimization.
Once you have decided on the approach and formulated your problem (either by collapsing your multiple objectives into a weighted one, or as series of linear programs) either tool will do the job for you.
Since you are familiar with MATLAB, you can start by using it to solve a series of linear programs (a goal programming approach). This page by Mathworks has a few examples with step-by-step details: http://www.mathworks.com/discovery/multiobjective-optimization.html to get you started.
Probably this question is not a matter of your current concern. However my answer is rather universal, so let me post it here.
If solving a multiobjective problem means deriving a specific Pareto optimal solution, then you need to solve a single-objective problem obtained by scalarizing (aggregating) the objectives. The type of scalarization and values of its parameters (if any) depend on decision maker's preferences, e.g. how he/she/you want(s) to prioritize different objectives when they conflict with each other. Weighted sum, achievement scalarization (a.k.a. weighted Chebyshev), and lexicographic optimization are the most widespread types. They have different advantages and disadvantages, so there is no universal recommendation here.
CPLEX is preferred in the case, where (A) your scalarized problem belongs to the class solved by CPLEX (obviously), e.g. it is a [mixed integer] linear/quadratic problem, and (B) the problem is complex enough for computational time to be essential. CPLEX is specialized in the narrow class of problems, and should be much faster than Matlab in complex cases.
You do not have to limit the choice of multiobjective methods to the ones offered by Matlab/CPLEX or other solvers (which are usually narrow). It is easy to formulate a scalarized problem by yourself, and then run appropriate single-objective optimization (source: it is one of my main research fields, see e.g. implementation for the class of knapsack problems). The issue boils down to finding a suitable single-objective solver.
If you want to obtain some general information about the whole Pareto optimal set, I recommend to start with deriving the nadir and the ideal objective vectors.
If you want to derive a representation of the Pareto optimal set, besides the mentioned population based-heuristics such as GAs, there are exact methods developed for specific classes of problems. Examples: a library implemented in Julia, a recently published method.
All concepts mentioned here are described in the comprehensive book by Miettinen (1999).
Can cplex solve a pareto type multiobjective one? All i know is that it can solve a simple goal programming by defining the lexicographical objs, or it uses the weighted sum to change weights gradually with sensitivity information and "enumerate" the pareto front, which highly depends on the weights and looks very subjective.
You can refer here as how cplex solves the bi-objetive one, which seems not good.
For a true pareto way which includes the ranking, i only know some GA variants can do like NSGA-II.
A different approach would be to use a domain-specific modeling language for mathematical optimization like YALMIP (or JUMP.jl if you like to give Julia a try). There you can write your optimization problem with Matlab with some extra YALMIP functionalities and use CPLEX (or any other supported solver as a backend) without restricting to one solver.
Do you know if anyone has tried to compile high level programming languages (java, c#, etc') into a recurrent neural network and then evolve them?
I mean that the whole process including memory usage is stored in a graph of a neural net, and I'm talking about complex programs (thinking about natural language processing problems).
When I say neural net I mean a directed weighted graphs that spreads activation, and the nodes are functions of their inputs (linear, sigmoid and multiplicative to keep it simple).
Furthermore, is that what people mean in genetic programming or is there a difference?
Neural networks are not particularly well suited for evolving programs; their strength tends to be in classification. If anyone has tried, I haven't heard about it (which considering I barely touch neural networks is not a surprise, but I am active in the general AI field at the moment).
The main reason why neural networks aren't useful for generating programs is that they basically represent a mathematical equation (numeric, rather than functional). Given some numeric input, you get a numeric output. It is difficult to interpret these in the context of a program any more complicated than simple arithmetic.
Genetic Programming traditionally uses Lisp, which is a pure functional language, and often programs are often shown as tree diagrams (which occasionally look similar to some neural network diagrams - is this the source of your confusion?). The programs are evolved by exchanging entire branches of a tree (a function and all its parameters) between programs or regenerating an entire branch randomly.
There are certainly a lot of good (and a lot of bad) references on both of these topics out there - I refrain from listing them because it isn't clear what you are actually interested in. Wikipedia covers each of these techniques, and is a good starting point.
Genetic programming is very different from Neural networks. What you are suggesting is more along the lines of genetic programming - making small random changes to a program, possibly "breeding" successful programs. It is not easy, and I have my doubts that it can be done successfully across a large program.
You may have more luck extracting a small but critical part of your program, one which has a few particular "aspects" (such as parameter values) that you can try to evolve.
Google is your friend.
Some sophisticated anti-virus programs as well as sophisticated malware use formal grammar and genetic operators to evolve against each other using neural networks.
Here is an example paper on the topic: http://nexginrc.org/nexginrcAdmin/PublicationsFiles/raid09-sadia.pdf
Sources: A class on Artificial Intelligence I took a couple years ago.
With regards to your main question, no one has ever tried that on programming languages to the best of my knowledge, but there is some research in the field of evolutionary computation that could be compared to something like that (but it's obviously a far-fetched comparison). As a matter of possible interest, I asked a similar question about sel-improving compilers a while ago.
For a difference between genetic algorithms and genetic programming, have a look at this question.
Neural networks have nothing to do with genetic algorithms or genetic programming, but you can obviously use either to evolve neural nets (as any other thing for that matters).
You could have look at genetic-programming.org where they claim that they have found some near human competitive results produced by genetic programming.
I have not heard of self-evolving and self-imrpvoing programs before. They may exist as special research tools like genetic-programming.org have but nothing solid for generic use. And even if they exist they are very limited to special purpose operations like malware detection as Alain mentioned.
I am writing programs that are based on robots navigating through mazes (would involve stochastic programming).
Since it will involve heavy matrix handling (plus point for MATLAB) and simulating a robot (plus point for Prolog), I am in a dilemma between the choice of MATLAB and Prolog.
Note: I do have MATLAB at my work environment, hence cost is not an issue.
As mentioned previously, I am not sure if you are looking for comparisons between MATLAB and Python or MATLAB and Prolog. I can speak to the former, at least: MATLAB provides fast linear algebraic computation and a great IDE... and that's about it. Python will cost you much fewer headaches (and dollars), and you can manage "heavy matrix handling" nearly as easily if you tack on Numpy in particular, or SciPy in general.
Also, VPython (Visual Python) is a great 3D visualization tool that uses Numpy under the hood. I developed a robot simulator using VPython; you can see screenshots and example code (for simple wall-following maze navigation) that you can check out in a recent blog post.