An Affine Scaling Interior Trust-Region Algorithm Combining Backtracking Line Search with Filter Technique for Nonlinear Constrained Optimization

Abstract

In this article, an affine scaling interior trust-region algorithm which employs backtracking line search with filter technique is presented for solving nonlinear equality constrained programming with nonnegative constraints on variables. At current iteration, the general full affine scaling trust-region subproblem is decomposed into a pair of trust-region subproblems in vertical and horizontal subspaces, respectively. The trial step is given by the solutions of the pair of trust-region subproblems. Then, the step size is decided by backtracking line search together with filter technique. This is different from traditional trust-region methods and has the advantage of decreasing the number of times that a trust-region subproblem must be resolved in order to determine a new iteration point. Meanwhile, using filter technique instead of merit function to determine a new iteration point can avoid the difficult decisions regarding the choice of penalty parameters. Under some reasonable assumptions, the new method possesses the property of global convergence to the first-order critical point. Preliminary numerical results show the effectiveness of the proposed algorithm.

Keywords:

• Filter technique
• Interior point
• Line search
• Nonlinear programming
• Trust-region method

Mathematics Subject Classification:

• 49M37
• 65K05
• 90C30
• 90C51
• 90C55

Notes

^a The numbers of iteration.

 ^b The numbers of function evaluations.

 ^c The numbers of gradient evaluations.