I am looking for a convenient Fortran function that works similarly to Matlab’s fmincon.
MINPACK doesn’t offer constrained minimization. It is also aimed primarily at solving least squares problems and solving nonlinear equations.
For constrained minimization take a loop at NLopt and it’s Fortran interface nlopt-f. Depending on the form of your constraints, and availability of an analytic Jacobian, I’d also recommend taking a look at Powell’s Derivative Free Optimizers, including bobyqa, lincoa, and cobyla. More optimization codes can be found in the NIST Guide to Available Mathematical Software (GAMS), Class G2: Constrained optimization
In case your Fortran routines will be used in conjuction with R, you could also take a look at R’s internal optimization routines, see Writing R Extensions - Optimization.
SOL SNOPT User Guide is primarily in Fortran. fmincon covers a lot of territory so not sure SNOPT applies. I thought it was freely available from Stanford University but a quick look on the web page says “Proprietary”; so no idea; but might be available for Academic use.
Take a look at this post: Optimization, root finding, and nonlinear equation solving
For constrained optimization, you would need something like SLSQP (free), SNOPT (not free) or VF13AD (freely available for download). IPOPT (free, non-trivial to compile though) is C++ but has a Fortran interface that works.
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Is SNOPT worth the 6240$ license fee for commercial use? How does it compare with other solvers? The trial licenses are limited to 3-months. A perpetual MATLAB license for commercial use costs 2100$ and a home license for personal use costs 119$. I have no doubt that successful optimization of an industrial problem can save a few thousand $ or more. But the price seems kind of high in comparison to other software packages.
@fortran4r, did you end up using any suggested packages? Is there any particular kind of bound constraint you need, e.g. box, linear, non-linear, equality?