Optimization Theory: The Finite Dimensional Case

By R. Paul, M. Hestenes. 1977

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Deep learning with Elastic Averaging SGD (2014, background): “The problem of the equivalence of these two objectives is studied in the literature and is known as the augmentability or the global variable consensus problem [8, 9].”
Second order optimality conditions in the smooth case and applications in optimal control (2007, background): “Legendre type conditions The following theorem is standard (see [3, 5, 7, 10, 19–21,25, 28]).”
Distributed stochastic optimization for deep learning (thesis) (2016, unknown): “The problem of the equivalence of these two objectives is studied in the literature and is known as the augmentability or the global variable consensus problem [24, 11].”
Neurobiology of Aging: Contents (2005, unknown): “11); that is, Â is J -symmetric (or pseudosymmetric: see Mackey, Mackey and Tisseur (2003)).”
Variable Selection using MM Algorithms. (2005, background): “This fact, together with the fact that ) is negative semideﬁnite, implies that the eigenvalues of ∇ M( β (k) ) are all contained in the interval [ 0 , 1 ) [13].”
Constant-Rank Condition and Second-Order Constraint Qualification (2010, background): “Some of them are, in order of weakness: quasinormality defined by Hestenes in [9], pseudonormality [10, 11], Abadie [12] and Guignard [13].”