Yes, JMP can! And I strongly advocate that one should learn how to use JMP's Nonlinear platform.
https://www.jmp.com/support/help/en/17.1/#page/jmp/launch-the-nonlinear-platform.shtml?os=win&source...
Learning how to use that tool will give you unlimited benefit for many years to come. It is a general purposed tool to optimize based on either least squares or maximum likelihood.
A colleague of mine asked me about the comparison of JMP Nonlinear platform with other optimization tools, such as the similar optimization functions in software like R and Matlab. My option is that JMP Nonlinear's capability is superior.
For example, one challenge to all such optimization is to find good starting values. Without good starting values, one usually has no clue about the quality of final results. But finding good starting values is usually an iterative process, and many times a guess game, if one cannot formally derive close proximity near solution. Use interactive tools in the platform, you can literally see how your initial guess, e.g. https://www.jmp.com/support/help/en/17.1/#page/jmp/example-of-the-nonlinear-platform.shtml# The interactive iteration is a much enjoyable process than trial-and-error command typing process in other software. And probably will give one the answer faster.
The platform is much richer than what I just described. It is a powerful and versatile tool!