libdogleg2

Powell's dog-leg nonlinear least squares solver for sparse matrices
  https://github.com/dkogan/libdogleg
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Solves unconstrained nonlinear least squares problems using powell's dog-leg method. the user specifies a callback c function that returns the value and gradients of the model function at a particular operating point. this library takes a series of dog-leg steps to find a local minimum of the residual surface.

this library works with sparse matrices, which makes it suitable for efficiently solving very large problems.