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Python bindings for TRON optimizer

Project description

The main function is pytron.minimize:

def minimize(func, grad_hess, x0, args=(), max_iter=1000, tol=1e-6):

    func : callable
        func(w, *args) is the evaluation of the function at w, It
        should return a float.
    grad_hess: callable
        returns the gradient and a callable with the hessian times
        an arbitrary vector.
    tol: float
        stopping criterion. XXX TODO. what is the stopping criterion ?

    w : array

Stopping criterion

It stops whenever ||grad(x)|| < eps or the maximum number of iterations is attained.

TODO: add tol



This software uses the C++ implementation of TRON optimization software (files src/tron.{h,cpp}) distributed from the LIBLINEAR sources (v1.93), which is BSD licensed. Note that the original Fortran TRON implementation (available here) is not open source and is not used in this project.

The modifications with respect to the orginal code are:

  • Do not initialize values to zero, allow arbitrary initializations

  • Modify stopping criterion to comply with scipy.optimize API. Stop whenever gradient is smaller than a given quantity, specified in the gtol argument

  • Return the gradient from TRON::tron (pass by reference)

  • Add tol option to TRON

  • Rename eps to gtol.

  • Use infinity norm as stopping criterion for gradient instead of L2.


  • return status from TRON::TRON

  • callback argument


If you use the software please consider citing some of the references below.

The method is described in the paper “Newton’s Method for Large Bound-Constrained Optimization Problems”, Chih-Jen Lin and Jorge J. Moré (

It is also discussed in the contex of Logistic Regression in the paper “Trust Region Newton Method for Logistic Regression”, Chih-Jen Lin, Ruby C. Weng, S. Sathiya Keerthi (

The website contains reference to this implementation, although the links to the software seem to be currently broken (May 2013).


This code is licensed under the terms of the BSD license. See file COPYING for more details.


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