Trust-region method (TRM) is one of the most important numerical optimization methods in solving nonlinear programming (NLP) problems. It works in a way that first define a region around the current best solution, in which a certain model (usually a quadratic model) can to some extent approximate the original objective function. TRM then take a step forward according to the model depicts within the region. Unlike the line search methods, TRM usually determines the step size before the improving direction (or at the same time). If a notable decrease (our following discussion will based on minimization problems) is gained after the step forward, then the model is believed to be a good representation of the original objective function. If the improvement is too subtle or even a negative improvement is gained, then the model is not to be believed as a good representation of the original objective function within that region. The convergence can be ensured that the size of the “trust region” (usually defined by the radius in Euclidean norm) in each iteration would depend on the improvement previously made.

Last modified

• 11/30/2018

Creator

• Wenhe (Wayne) Ye

DOI

• https://doi.org/10.21985/N2TN0H

Keyword

• programming
• Trust-region

Rights statement

• In Copyright