Défense de thèse de doctorat en sciences mathématiques: "numerical optimization", une thèse du centre naXys

A trust-region method for constrained derivative-free optimization and worst-case evaluation complexity of non-monotone gradient-related algorithms for unconstrained optimization

Jury

Andrew CONN (IBM), Serge GRATTON (ENSEEIHT), Anne LEMAITRE, présidente (UNamur), Annick SARTENAER (UNamur), Philippe TOINT, promoteur (UNamur)

Résumé

The thesis is concerned with numerical optimization, i.e. the design, analysis and implementation of algorithms whose purpose is to find a "best" solution of a problem (in the sense that the value of an "objective function" is optimal) in a set of possible ones defined by "constraints". The work is divided into two parts related to two research topics which have received increasing attention of the optimization community over the past years. The first part is concerned with the design and implementation of a new trust-region method for constrained optimization which does not require derivatives of the objective function or constraints.  This method is based on interpolation models and employs a self-correcting geometry procedure in order to ensure that the geometry of the interpolation set does not differ too much from the ideal one. Numerical results of the proposed method are also presented and show that it compares favorably to competing algorithms. The second part analyzes the worst-case evaluation complexity of the class of non-monotone gradient-related algorithms for smooth nonconvex and unconstrained problems. We show that the number of function evaluations needed to find a point with the gradient norm below a certain threshold is at most proportional to the inverse of the threshold squared.

La défense est publique.

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