In ETNA* we propose new local convex approximations for solving unconstrained non-linear optimization problems based on a moving asymptotes algorithm. This method incorporates second-order information for the moving asymptotes location. As a consequence, at each step of the iterative process, a strictly convex approximation subproblem is generated and solved. All subproblems have explicit global optima. This considerably reduces the computational cost of our optimization method and generates an iteration sequence. For this method, we prove convergence of the optimization algorithm under basic assumptions.
This gitHub repository is dedicated to implementation of an application to test such methods on nonlinear, non-convex optimization problems.
(*) A moving asymptotes algorithm using new local convex approximation methods with explicit solutions, Mostafa Bachar, Thierry Estebenet, and Allal Guessab, ETNA Volume 43, pp. 21-44, 2014-2015.