Derivative-free separable quadratic modeling and cubic regularization for unconstrained optimization

Custódio, A. L.; Garmanjani, R.; Raydan, M.

http://hdl.handle.net/10362/162115

Utilize este identificador para referenciar este registo.

Nome:	Descrição:	Tamanho:	Formato:
Derivative-free_separable_quadratic_modeling.pdf		533.9 KB	Adobe PDF	Ver/Abrir

Contacte-nos

Autores

Custódio, A. L.

Garmanjani, R.

Raydan, M.

Resumo(s)

We present a derivative-free separable quadratic modeling and cubic regularization technique for solving smooth unconstrained minimization problems. The derivative-free approach is mainly concerned with building a quadratic model that could be generated by numerical interpolation or using a minimum Frobenius norm approach, when the number of points available does not allow to build a complete quadratic model. This model plays a key role to generate an approximated gradient vector and Hessian matrix of the objective function at every iteration. We add a specialized cubic regularization strategy to minimize the quadratic model at each iteration, that makes use of separability. We discuss convergence results, including worst case complexity, of the proposed schemes to first-order stationary points. Some preliminary numerical results are presented to illustrate the robustness of the specialized separable cubic algorithm.

Descrição

Open access funding provided by FCT|FCCN (b-on). The first and second authors are funded by national funds through FCT - Fundação para a Ciência e a Tecnologia I.P., under the scope of projects PTDC/MAT-APL/28400/2017, UIDP/MAT/00297/2020, and UIDB/MAT/00297/2020 (Center for Mathematics and Applications). The third author is funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects CEECIND/02211/2017, UIDP/MAT/00297/2020, and UIDB/MAT/00297/2020 (Center for Mathematics and Applications). Publisher Copyright: © 2023, The Author(s).

Palavras-chave

Cubic regularization Derivative-free optimization Fully-linear models Fully-quadratic models Worst-case complexity Management Information Systems Theoretical Computer Science Management Science and Operations Research Computational Theory and Mathematics