An efficient implementation of a trust region method for box constrained optimization

The present research deals with a trust-region-based procedure to solve box constrained optimization problems. Our procedure takes the advantage of the compact limited memory BFGS update formula together with an adaptive radius strategy. This adaptive technique leads to decreasing the number of solved subproblems and the total number of iterations, while utilizing the structure of limited memory quasi-Newton formula helps us to handle large-scale problems. Using classical assumptions, we prove that our method is a global convergence to first-order stationary points. Preliminary numerical experiments indicate that our new approach is considerably promising to solve box constrained optimization problems, especially for large-scale ones.

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