HP2C and the Università della Svizzera Italiana (USI) are happy to present a talk of Philippe Toint on Cubic regularization algorithm and complexity issues for nonconvex optimization (August 2010).
We consider regularization methods for the nonconvex unconstrained and convexely constrained optimization problems. After motivating these algorithms, we review known convergence results and emphasize their remarkabke complexity properties, that is the number of function evaluations that are needed for the algorithm to produce an epsilon-critical point. We also discuss the complexity of the well-known steepest-descent and Newton’s method in the unconstrained case and report some surprising conclusions regarding their relative complexity.
Philippe Toint is director of the Department of Mathematics of the University of Namur (Belgium), co-director of the Numerical Analysis Research Unit, director of the Transportation Research Group. Chairman elect (2010-2012) of the Mathematical Optimization Society , SIAM fellow (class 2009) and Honorary Professor at the University of Edinburgh.
His research interests are smooth nonlinear optimization, with an emphasis on the algorithmic viewpoint, ranging from convergence theory to numerical considerations and software development ( LANCELOT, CUTEr, GALAHAD ). Practical and multidisciplinary applications of optimization techniques.