Journal of Systems Science and Complexity

, Volume 27, Issue 3, pp 537–564

# An affine scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming

• Jing Gao
• Detong Zhu
Article

## Abstract

This paper proposes an affine scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm.

## Key words

Affine scaling backtracking technique box constrains derivative-free optimization nonlinear programming trust region method.

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