A derivative-free affine scaling trust region methods based on probabilistic models with new nonmonotone line search technique for linear inequality constrained minimization without strict complementarity

ABSTRACT

In this paper, a derivative-free trust region methods based on probabilistic models with new nonmonotone line search technique is considered for nonlinear programming with linear inequality constraints. The proposed algorithm is designed to build probabilistic polynomial interpolation models for the objective function. We build the affine scaling trust region methods which use probabilistic or random models within a classical trust region framework. The new backtracking linear search technique guarantee the descent of the objective function, and new iterative points are in the feasible region. In order to overcome the strict complementarity hypothesis, under some reasonable conditions which are weaker than strong second order sufficient condition, we give the new and more simple identification function to structure the affine matrix. The global and local fast convergence of the algorithm are shown and the results of numerical experiments are reported to show the effectiveness of the proposed algorithm.

KEYWORDS:

• Derivative-free optimization
• affine matrix
• nonlinear programming
• probabilistic models
• global convergence
• nonmonotone linear search

2010 MSC CLASSIFICATIONS:

• 49M37
• 65K05
• 90C30
• 90C56

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors gratefully acknowledge the partial supports of the National Science Foundation of China [Grant 11371253]. The authors gratefully acknowledge the partial supports of the Natural Science Foundation of Hainan province [Grant 117107].