An affine scaling interior trust-region method combining with line search filter technique for optimization subject to bounds on variables

• Published in: Numerical algorithms Vol. 77; no. 4; pp. 1159 - 1182
• Main Authors: Li, Dan, Zhu, Detong
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2018; Springer Nature B.V
• Subjects: Algebra; Algorithms; Computer Science; Convergence; Iterative methods; Methods; Numeric Computing; Numerical Analysis; Optimization; Original Paper; Quadratic equations; Scaling; Searching; Theory of Computation; Trust-region; Line search; 65K05; 90C30; Nonlinear optimization; 49M37; Interior point; Filter method
• ISSN: 1017-1398; 1572-9265
• DOI: 10.1007/s11075-017-0357-2

This paper proposes and analyzes an affine scaling trust-region method with line search filter technique for solving nonlinear optimization problems subject to bounds on variables. At the current iteration, the trial step is generated by the general trust-region subproblem which is defined by minimizing a quadratic function subject only to an affine scaling ellipsoidal constraint. Both trust-region strategy and line search filter technique will switch to trail backtracking step which is strictly feasible. Meanwhile, the proposed method does not depend on any external restoration procedure used in line search filter technique. A new backtracking relevance condition is given which is weaker than the switching condition to obtain the global convergence of the algorithm. The global convergence and fast local convergence rate of this algorithm are established under reasonable assumptions. Preliminary numerical results are reported indicating the practical viability and show the effectiveness of the proposed algorithm.