On fast trust region methods for quadratic models with linear constraints

: Quadratic models Qk(x), x ∈ Rn , of the objective function F(x), x∈Rn , are used by many successful iterative algorithms for minimization, where k is the iteration number. Given the vector of variables xk ∈ Rn , a new vector xk+1 may be calculated that satisfies Qk(xk+1) < Qk(xk), in the hope that it provides the reduction F(xk+1) < F(xk). Trust region methods include a bound of the form xk+1 −xk ≤ ∆k. Also we allow general linear constraints on the

• Type: Journal
• Year: 2015
• Where: MPC
• Authors: M. J. D. Powell
• Keywords: Mathematics, MPC 2015