UOBYQA: unconstrained optimization by quadratic approximation

UOBYQA is a new algorithm for general unconstrained optimization calculations, that takes account of the curvature of the objective function, F say, by forming quadratic models by interpolation. Therefore, because no first derivatives are required, each model is defined by 1 2 (n+1)(n+2) values of F, where n is the number of variables, and the interpolation points must have the property that no nonzero quadratic polynomial vanishes at all of them. A typical iteration of the algorithm generates a new vector of variables, xt say, either by minimizing the quadratic model subject to a trust region bound, or by a procedure that should improve the accuracy of the model. Then usually F(xt) is obtained, and one of the interpolation points is replaced by xt. Therefore the paper addresses the initial positions of the interpolation points, the adjustment of trust region radii, the calculation of xt in the two cases that have been mentioned, and the selection of the point to be replaced. Further, ...

• Type: Journal
• Year: 2002
• Where: MP
• Authors: M. J. D. Powell
• Keywords: Interpolation Point, MP 2002, Quadratic Model, Unconstrained Optimization Calculations