A Subspace Minimization Method for the Trust-Region Step

A Subspace Minimization Method for the Trust-Region Step

We consider methods for large-scale unconstrained minimization based on finding an approximate minimizer of a quadratic function subject to a two-norm trust-region constraint. The Steihaug–Toint method uses the conjugate-gradient method to minimize the quadratic over a sequence of expanding subspaces until the iterates either converge to an interior point or cross the constraint boundary. Howev...

An Interior-point Subspace Minimization Method for the Trust-region Step

Abstract. We consider methods for large-scale unconstrained minimization based on finding an approximate minimizer of a quadratic function subject to a two-norm trust-region inequality constraint. The Steihaug-Toint method uses the conjugate-gradient algorithm to minimize the quadratic over a sequence of expanding subspaces until the iterates either converge to an interior point or cross the co...

A subspace trust-region method for seismic migration inversion

In seismic exploration, regularized migration inversion of seismic data usually requires solving a weighted least-squares problem with constrains. It is well known that directly solving this problem using some decomposition techniques is very time-consuming, which makes it less possible for practical use. For iterative methods, previous research is mainly on solving the inverse model in a full ...

A Recursive Trust–Region Method for Non–convex Constrained Minimization

A Second-derivative Trust-region Sqp Method with a “trust-region-free” Predictor Step

In (NAR 08/18 and 08/21, Oxford University Computing Laboratory, 2008) we introduced a second-derivative SQP method (S2QP) for solving nonlinear nonconvex optimization problems. We proved that the method is globally convergent and locally superlinearly convergent under standard assumptions. A critical component of the algorithm is the so-called predictor step, which is computed from a strictly ...