Optimizing Partially Separable Functions Without Derivatives
by B. Colson and Ph. L. Toint
Report 2003/20
We present an algorithm for solving nonlinear programming problems involving a
partially separable objective function whose derivatives are assumed to be
unavailable. At each iteration we construct a quadratic interpolation model
of the objective function around the current iterate and minimize this model
to obtain a trial step. The whole process is embedded within a trust-region
framework. We further propose to use ideas of Curtis, Powell and Reid to
minimize the number of calls to the objective function in the part of the
derivative-free algorithm that improves the geometry of the interpolation
set. Numerical experiments tend to confirm the promising behaviour of the
algorithm.
Keywords: partially separable functions, derivative-free
optimization, multivariate interpolation, trust-region algorithms.