Worst case complexity of direct search

• Author(s): Vicente, L. N.
• Date: 2010
• Persistent ID: http://hdl.handle.net/10316/13699
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Derivative-free optimization; Direct search; Worst case complexity; Sufficient decrease
• Document Type: Preprint
• Language: English

Description

In this paper we prove that direct search of directional type shares the worst case complexity bound of steepest descent when sufficient decrease is imposed using a quadratic function of the step size parameter. This result is proved under smoothness of the objective function and using a framework of the type of GSS (generating set search). We also discuss the worst case complexity of direct search when only simple decrease is imposed and when the objective function is non-smooth.