Abstract

In this talk, we review various subspace techniques that are used in constructing of numerical methods for nonlinear optimization. The subspace techniques are getting more and more important as the optimization problems we have to solve are getting larger and larger in scale. Subspace techniques have the advantage of reducing both computation cost and memory size. The essential part of a subspace method is how to choose the subspace in which the trial step or the trust region should belong. Examples of applications of subspace techniques are also presented.