In this talk, we consider the problem of minimizing a smooth function over the symplectic Stiefel manifold. To address this problem, we propose a feasible gradient method based on a novel retraction. The operation that requires the highest computational cost to compute the proposed retraction is the inversion of a 2p-by-2p matrix, which is much less expensive than those required for the existing  retractions. In order to improve the numerical performance of our approach, we use the non-monotone globalization strategy of Zhang and Hager equipped with an adaptive Barzilai-Borwein step-size. Our numerical studies show that the proposed procedure is computationally promising and competes favorably with other first-order methods existing in the literature.

Joint work with: 

PhD. Rafael Herrera. Department of Mathematics, Centro de Investigación em Matemáticas A.C. (CIMAT), Mexico.

I. Seminar participants will not be able to access FGV premises wearing shorts, flip-flops, top or cropped tshirts, miniskirt or tank top. The use of the mask and the presentation of proof of vaccination (physical or digital) will be mandatory.  II. Text provided by the author.