×

Active-set strategy in Powell’s method for optimization without derivatives. (English) Zbl 1215.90046

Summary: In this article we present an algorithm for solving bound constrained optimization problems without derivatives based on M. J. D. Powell’s method [in: G. Di Pillo (ed.) et al., Large-scale nonlinear optimization. New York, NY: Springer. Nonconvex Optimization and Its Applications 83, 255–296 (2006; Zbl 1108.90005)] for derivative-free optimization. First we consider the unconstrained optimization problem. At each iteration a quadratic interpolation model of the objective function is constructed around the current iterate and this model is minimized to obtain a new trial point. The whole process is embedded within a trust-region framework. Our algorithm uses infinity norm instead of the Euclidean norm and we solve a box constrained quadratic subproblem using an active-set strategy to explore faces of the box. Therefore, a bound constrained optimization algorithm is easily extended. We compare our implementation with NEWUOA and BOBYQA, Powell’s algorithms for unconstrained and bound constrained derivative free optimization respectively. Numerical experiments show that, in general, our algorithm require less functional evaluations than Powell’s algorithms.

MSC:

90C30 Nonlinear programming
90C56 Derivative-free methods and methods using generalized derivatives
90-08 Computational methods for problems pertaining to operations research and mathematical programming

Citations:

Zbl 1108.90005
PDFBibTeX XMLCite