References
- A
bsil , P.-A., Mahony , R.,and Sepulchre , R. (2008) Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton, N.J., Woodstock. - A
ssouad , P. (1983) Plongements Lipschitziens dans Rn. Bull. Soc. Math. France 111, 429–448. - A
ubin , J.P.and Frankowska , H. (1990) Set-Valued Analysis. Birkhäuser, Boston. - B
aydin , A.G., Pearlmutter , B.A., Radul , A.A.,and Siskind , J.M. (2018) Automatic differentiation in machine learning: A survey. Journal of Machine Learning Research, 18, 1–43. - B
olte , J.and Pauwels , E. (2021) Conservative set valued fields, automatic differentiation, stochastic gradient methods and deep learning. Mathematical Programming: Series A and B. 188 (1), 19–51. - D
elfour , M.C. (2016) Differentials and semidifferentials for metric spaces of shapes and geometries. In: System Modeling and Optimization, L. Bociu, J.-A. Désidéri and A. Habbal, eds., 230–239, Springer International Publishing AG, Switzerland. - D
elfour , M.C. (2018a) Topological derivative: a semidifferential via the Minkowski content. Journal of Convex Analysis 25 (3), 957–982. - D
elfour , M.C. (2018b) Control, shape, and topological derivatives via minimax differentiability of Lagrangians. In: Numerical Methods for Optimal Control Problems. M. Falcone, R. Ferretti, L. Grüne, W. McEneaney, eds., 137–164, Springer INdAM Series 29, Springer, Cham, Switzerland. - D
elfour , M.C. (2020a) Introduction to Optimization and Hadamard Semi-differential Calculus, 2nd ed. SIAM, Philadelphia, PA. - D
elfour , M.C. (2020b) Hadamard semidifferential of functions on an unstructured subset of a TVS. J. Pure Appl. Funct. Anal. 5 (5), 1039–1072. - D
elfour , M.C. (2023a) One-sided Derivative of Parametrized Minima for Shape and Topological Derivatives. SIAM J. Control. Optim. 61 (3), 1322–1349. - D
elfour , M.C. (2023b) Hadamard semidifferential of continuous convex functions. J. Pure and Applied Functional Analysis 8 (5), 1341–1356. - D
elfour , M.C.and Huot -Chantal , F. (2019) On the figure of columns of Lagrange revisited. J. Convex Anal. (3)26, 855–876. - D
elfour , M.C.and Zolésio , J.P. (2011) Shapes and Geometries: Metrics, Analysis, Differential Calculus and Optimization, 2nd ed. SIAM, Philadelphia, PA. - E
delman , A., Arias , T.A.and Smith , S.T. (1998) The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl. 20 (2), 303–353. - E
vans , L.C.and Gariepy , R.F. (1992) Measure Theory and the Properties of Functions. CRC Press, Boca Raton, FL. - F
réchet , M. (1937) Sur la notion de différentielle. Journal de Mathématiques Pures et Appliquées 16, 233–250. - G
romov , M. (1991) Geometric Group Theory, volume 2: Asymptotic Invariants of Infinite Groups. London Mathematical Society Lecture Note Series, 182, Cambridge University Press. - H
orváth , J. (1966) Topological Vector Spaces and Distributions, Vol. I. Addison-Wesley, Reading, MA. - H
uot -Chantal , F. (2018) Sur la figure des colonnes de Lagrange revisité. Mémoire, Dép. de Mathématiques et de Statistique, Université de Montréal, Canada. - J
i , M.and Klinowski , J. (2006) Taboo evolutionary programming: a new method of global optimization. Proc. R. Soc. A 462, 3613–3627. - L
ang , S. (1969) Analysis II. Addison–Wesley Publishing Company, Reading, Mass. - L
ange , K. (2024) A tutorial on Hadamard semidifferentials. Foundations and Trends in Optimization 6 (1), 1–62. - M
arsden , J.E.and Ratiu , T.S. (1994) Introduction to Mechanics and Symmetry. Springer-Verlag, New York, Berlin. - M
ichor , P.W.and Mumford , D. (2013) A zoo of diffeomorphism groups on ℝn. Ann. Glob. Anal. Geom. 44 (4), 529–540. - N
eidinger , R. D. (2010) Introduction to automatic differentiation and matlab object-oriented programming. SIAM Review, 52, 545–563. - P
ansu , P. (1989) Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un. Ann. of Math. 129 (2), 1–60. - P
oinsot , L. (2017) Lipschitz groups and Lipschitz maps. International Journal of Group Theory 6 (1), 9–16. - R
udin , W. (1976) Principles of Mathematical Analysis. McGraw–Hill, New York.