The PATH solver: changing options - matlab

The PATH solver is a MATLAB program for solving the linear complementarity problem.
In this solver, users can change default options such as stopping criterion (1e-6); however, I cannot find how to change options in MATLAB.
Could you tell me the way of changing these settings?

Related

Interior-point linear programing solver in MATLAB, with target barrier parameter option

Is there any linear programing solver, written for MATLAB, that (a) solves with the primal-dual interior point method, (b) the user has the options to set the target barrier parameter (he lowest value of barrier parameter for which the KKT system is solved)?
I currently use IPOPT, which has the target barrier parameter options.
However, at convergence, the product of dual*slack seems to only be approximately satisfied (with an error of say (+-)1e-7 for a target parameter of 1e-5).
I have tried to play around with the tolerances, but to no avail.
For MATLAB use, I recommend using CVX, which includes Gurobi, MOSEK, GLPK, and SDPT3. All of those can solve the linear program very efficiently.
CVX is very easy to use in MATLAB.

How to deal with failure to solve nonlinear equations during simulation in Dymola?

I build a model of solar power plant with the Rankine cycle in Dymola, even though the initialization works fine, but at the time of 2840s, there is a failure to solve the nonlinear equations which leads the simulation to stop.
As shown in the following screenshot, Dymola recommends giving better start values, but it doesn't make any sense, because the failure happens during the simulation instead of initialization. And with better start values, the situation doesn't improve at all.
My question is :
How should I deal with the failure to solve nonlinear equations during simulation?
The error message indicates that the solver was not able to find a solution to a nonlinear system of equations in your model. This could mean either that there is no solution to the system or just that the solver is not able to find it.
The first easy steps would be to try a lower tolerance in simulation settings. And to use another solver that might suit better for your problem. Dassl can handle nonlinear systems quite well. If these steps won't work it might be that there just isn't a solution to your problem and you made a wrong assumption or accidentially have a wrong parameter somewhere.

How to set up a large set of first order non-linear differential equations in Matlab?

I am relatively new to writing my own code for Matlab though I have used the program a decent amount. Right now I am attempting to code a series of first order non-linear differential equations. They are all in one of two forms like the equations here:
Eventually I will need a set of 30 differential equations.
What I was hoping to do was create a function that could make the differential equation for each component of a certain form, combine them into a single system (essentially a matrix with 1 column and a row for each component), and then solve using a Matlab solver like ODE45, the dsolve function, or something like that to solve the system.
I have not yet found a way to make a function set up this large of a system that works with either dsolve or ODE45. The results always either gave me an empty sym or an error that the initial conditions were not compatible with the system or some other error. So what I am wondering is if there is another way to go about setting up a system that is this large and has nonlinear differential equations.
I do not want someone else's code; I just want an idea for how to go about setting this up in Matlab because nothing I have tried has worked so far.

Some issues with fmincon in matlab

I was using Matlab's fmincon but the optimization stopped with the following message
fmincon stopped because the size of the current step is less than
the selected value of the step size tolerance.
I have TolX set to 10^-10 and Tolfun to 10^-10 as well
I checked the logs and the first-order optimality was 198. Therefore this is definitely not the optimum solution. What could possibly go wrong?
Further, I used different version of matlab R2013b and R2014a and for the same code and data, they have different results. Is there something wrong with fmincon in matlab R2013b?
When you have a question about the difference between two versions of Matlab or, as in this case, two toolbox versions, the first place to check is release notes: for Matlab and for the Optimization toolbox. Indeed, it seems that fmincon was updated. Do you specify an 'Algorithm'? If not, the difference may be due the different default in R2014a. In this case, you may be able to specify the use of the 'interior-point' algorithm in R2013b and get better results.
You can read about the algorithms used by fmincon here.

By setting a tspan=[to:very_small_step:tf], can it affect ode45 solver's step size?

I have know that the ode45 solver has adaptive step size controlled by Matlab program itself. The description below is given by Matlab website:
Specifying tspan with more than two elements does not affect the internal time steps that >the solver uses to traverse the interval from tspan(1) to tspan(end). All solvers in the ODE >suite obtain output values by means of continuous extensions of the basic formulas. Although >a solver does not necessarily step precisely to a time point specified in tspan, the >solutions produced at the specified time points are of the same order of accuracy as the >solutions computed at the internal time points.
However, if I specify very_small_step in tspan=[to:very_small_step:tf], will this affect program controlled step size. Will this force step size less than the value of very_small_step? OR matlab will make interpolation calculation to get the corresponding result at specified time point?
From your quote
Specifying tspan with more than two elements does not affect the internal time steps
Also there exists the MaxStep property to configure the maximum step size.
For steps in between the solvers use continuous extension formulas as described here.
Why are you asking anyway? What problem do you encounter?