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Cubic regularization algorithm and complexity issues for nonconvex optimization

Community HP2C
Thursday 19 August 2010, 14:00 - 16:00, hosted by Università della Svizzera italiana (USI)


Prof. Dr. Philippe Toint


Thursday, August 19th, 2010


University of Lugano, room SI-008, Informatics building (Via G. Buffi 13)




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.