An affine scaling interior trust-region method combining with nonmonotone line search filter technique for linear inequality constrained minimization

ABSTRACT

This paper proposes an affine scaling interior trust-region method in association with nonmonotone line search filter technique for solving nonlinear optimization problems subject to linear inequality constraints. Based on a Newton step which is derived from the complementarity conditions of linear inequality constrained optimization, a trust-region subproblem subject only to an ellipsoidal constraint is defined by minimizing a quadratic model with an appropriate quadratic function and scaling matrix. The nonmonotone schemes combining with trust-region strategy and line search filter technique can bring about speeding up the convergence progress in the case of high nonlinear. A new backtracking relevance condition is given which assures global convergence without using the switching condition used in the traditional line search filter technique. The fast local convergence rate of the proposed algorithm is achieved which is not depending on any external restoration procedure. The preliminary numerical experiments are reported to show effectiveness of the proposed algorithm.

KEYWORDS:

• Nonlinear optimization
• trust-region
• line search
• filter method
• interior point

2010 MSC:

• 49M37
• 65K05
• 90C30

Acknowledgments

We are very grateful to the anonymous reviewers for their valuable and insightful comments and suggestions, which have helped us to improve the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Dan Li http://orcid.org/0000-0001-5545-3574

Additional information

Funding

The authors gratefully acknowledge the partial supports of the National Natural Science Foundation of China [grant number 11371253].