A class of derivative-free trust-region methods with interior backtracking technique for nonlinear optimization problems subject to linear inequality constraints

• Published in: Journal of inequalities and applications Vol. 2018; no. 1; pp. 108 - 22
• Main Authors: Gao, Jing, Cao, Jian
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 2018; Springer Nature B.V; SpringerOpen
• Subjects: Affine scaling; Algorithms; Analysis; Applications of Mathematics; Convergence; Derivative-free optimization; Inequality constraints; Interior backtracking technique; Linear functions; Mathematical analysis; Mathematics; Mathematics and Statistics; Nonlinear programming; Optimization; Trust-region method; 90C51; 65K05; 90C30; Affine scaling; Trust-region method; Interior backtracking technique; 49M37; Inequality constraints; Derivative-free optimization
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-018-1698-7

This paper focuses on a class of nonlinear optimization subject to linear inequality constraints with unavailable-derivative objective functions. We propose a derivative-free trust-region methods with interior backtracking technique for this optimization. The proposed algorithm has four properties. Firstly, the derivative-free strategy is applied to reduce the algorithm’s requirement for first- or second-order derivatives information. Secondly, an interior backtracking technique ensures not only to reduce the number of iterations for solving trust-region subproblem but also the global convergence to standard stationary points. Thirdly, the local convergence rate is analyzed under some reasonable assumptions. Finally, numerical experiments demonstrate that the new algorithm is effective.