Publications of Guillaume Olikier

1. Guillaume Olikier, Kyle Gallivan, and P. -A. Absil. Low-rank optimization methods based on projected-projected gradient descent that accumulate at Bouligand stationary points. Mathematics of Operations Research, April 2026. Keyword(s): Clarke regularity, tangent and normal cones, steepest descent, determinantal variety, low-rank optimization, critical point, stationary point, convergence analysis. [bibtex-entry]



2. Guillaume Olikier, Petar Mlinaric, P. -A. Absil, and André Uschmajew. The tangent cone to the real determinantal variety: various expressions and a proof. Set-Valued and Variational Analysis, 34(2):8, March 2026. Keyword(s): low-rank matrices, tangent cone, determinantal variety. [bibtex-entry]



3. Guillaume Olikier and Irène Waldspurger. Projected gradient descent accumulates at Bouligand stationary points. SIAM Journal on Optimization, 35(2):1004-1029, March 2024. Keyword(s): Clarke regularity, Tangent and normal cones, Stationarity, Projected gradient descent. [bibtex-entry]

1. Tom Szwagier, Guillaume Olikier, and Xavier Pennec. Eigengap Sparsity for Covariance Parsimony. In Proc. of the 7th International Conference on Geometric Science of Information - GSI'25, volume LNCS 16034 of Lecture Notes in Computer Science, Saint-Malo (35400), France, pages pp 50-59, October 2025. Keyword(s): Isotonic regression, Monotone cone, Flag manifolds, Eigengaps, Parsimony, Covariance estimation. [bibtex-entry]



2. Guillaume Olikier. Retractions on closed sets. In IFAC-PapersOnLine, volume 58, Cambridge (GB), United Kingdom, pages 286-291, August 2024. Keyword(s): retraction, tangent cones, stationarity, line-search methods, low-rank optimization. [bibtex-entry]

1. Guillaume Olikier and P. -A. Absil. Computing Bouligand stationary points efficiently in low-rank optimization. Note: Working paper or preprint, September 2024. Keyword(s): convergence analysis, stationary point, critical point, low-rank optimization, determinantal variety, first-order method, tangent cones, singular value decomposition, QR factorization. [bibtex-entry]

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