Nonmonotone trust region method for solving optimization problems (Q1886565)

The author proposes a trust region method with nonmonotone technique for unconstrained optimization problems of the form \[ \min f(x)\quad\text{s.t. }x\in\mathbb{R}^n. \] A new ratio of actual descent and predicted descent is constructed which is a simple generalization of the modified Armijo line search rule. The application to equality constrained and nonsmooth optimization problems is discussed.