A First-Order Convergence Analysis of Trust-Region Methods with Inexact Jacobians

A class of trust-region algorithms is developed and analyzed for the solution of minimization problems with nonlinear inequality constraints. Based on composite-step trust region methods with barrier functions, the resulting algorithm also does not require the computation of exact Jacobians; only Jacobian vector products are used along with approximate Jacobian matrices. As demonstrated on numerical examples, this feature has significant benefits for problems where Jacobian calculations are expensive. keywords Trust-region algorithms, inexact Jacobians, inequality constraints, global convergence

• Type: Journal
• Year: 2008
• Where: SIAMJO
• Authors: Andrea Walther
• Keywords: Approximate Jacobian Matrices, Inequality Constraints, Nonlinear Inequality Constraints, SIAMJO 2008