There cannot exist a finite number of distinct minimizers that are not connected.Ģ) Polynomials have a distinct number of roots that we can uniquely determine. As for C/C++, there are a variety of options. Find the algorithm that works best for your problem. In some cases the solver automatically switches algorithms with a warning message an you can specify the algorithm to use via optimset. The exception is that technically, there can exist an infinite number of solutions, but they will all be connected (like on a specific plane). Matlab's fsolve uses a trust region method by default, the Trust-Region Dogleg method. Furthermore, this minimizer is almost always unique. So anything returned by fsolve will be a global minimizer. So basically, there is no way of doing what you want except for 2 well known cases:ġ) If the problem is convex, then there are no local minimizers that are not global minimizers. On the hand, almost all other optimization solvers are local, meaning that they will only guarantee that a local minimizer is returned.įurthermore, in addition to not knowing whether the returned solution is a global or local minimizer, there is, in general, no way of determining how many roots a problem has. There are global solvers (like genetic algorithms and simulated annealing), but they have to run for an infinite amount of time to guarantee that the returned solutions comprise all of the minimizers. There are many others, such as PNL and the quite interesting-looking O 2scl ( documentation).Fsolve is not a global solver. For example, it appears that MINPACK implements a Powell dogleg algorithm similar to fsolve's default method. fsolve completed because the vector of function values is near zero as measured by the default value of the function tolerance, and the problem appears regular as measured by the gradient. You might look for code that implements the same or similar algorithm as you're using in fsolve. Whenever fsolve finishes, it gives the output. The GSL has support for multi-dimensional root-finding. Find the algorithm that works best for your problem.Īs for C/C++, there are a variety of options. Matlab's fsolve uses a trust region method by default, the Trust-Region Dogleg method. By adjusting the initial guess (here x0) or using using more advanced constrained optimization, the other roots can be found. Note that for these parameters, this system has multiple roots, but numeric methods generally only return one root. I noted that the fsolve gives just one root. I have two nonlinear equations with two variables (x,y) I'm trying to find the all possible roots for the both variables. Which returns a single root with coordinates at x = I'm using MATLAB's fsolve function to solve systems of nonlinear equations. You should probably start by ensuring that you can solve your problem in Matlab using this function – here's an example: a = In Matlab, fsolve ( documentation) performs this function. For your example, you need a multi-dimensional nonlinear root-solver. If your parameters are given in terms of floating-point values and you're ultimately interested in obtaining a floating-point value as a result, numeric methods should be your first choice (there are reasons to use symbolic approaches, but I'm not going to discuss this here). You probably don't need to be using symbolic math in Matlab in the first place.
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