Lectures on Convex Optimization

By Yurii E. Nesterov. 2018

1,273 citations recorded by the source corpus.

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Citations in the corpus

Second-order Conditional Gradients (2020, positive): “(Nesterov, 2018)[Lemma 4.1.1] If a twice differentiable function f has L2-Lipschitz continuous Hessian over X then for all x,y ∈ X :∥∥∇f(y)−∇f(x)−∇2f(x) (y − x)∥∥ ≤ L2 2 ‖y − x‖2 .”
COCO: a platform for comparing continuous optimizers in a black-box setting (2016, background): “In this paper we only consider zero-order black-box optimization [19, 57, 58]: while the search domain X ⊂ Rn and its boundaries are accessible, no other prior knowledge about f is available to the solver.”
The Frank-Wolfe Algorithm: A Short Introduction (2023, neutral): “Projection-based ﬁrst-order methods have been extensively studied, with comprehensive overviews available in, e.g., Nesterov [67], Nocedal and Wright [68].”
Rényi Fair Inference (2019, positive): “Thus according to (Nesterov, 2018, Chapter 1), the algorithm finds a point with ‖∇gB(θ)‖ ≤ in O( −2) iterations.”
SCAFFOLD: Stochastic Controlled Averaging for Federated Learning (2019, background): “…(A5) also implies the following quadratic upper bound on f i If additionally the function { f i } are convex and x (cid:63) is an optimum of f , (A5) implies (via Nesterov (2018), Theorem 2.1.5) Further, if f i is twice-differentiable, (A5) implies that (cid:107)∇ 2 f i ( x ) ≤ β for any x .”
Stochastic Mirror Descent: Convergence Analysis and Adaptive Variants via the Mirror Stochastic Polyak Stepsize (2021, background): “If f happens to be convex and L -smooth with respect to a norm (Nesterov, 2018)[Theorem 2.1.5], providing a similar convergence guarantee on the distance of gradients to ∇ f ( x ∗ ).”
On the Global Convergence Rates of Softmax Policy Gradient Methods (2020, positive): “In retrospect, perhaps this is unsurprising as entropy regularization bears a strong similarity to introducing a strongly convex regularizer in convex optimization, where this change is known to significantly improve the rate of convergence of first-order methods (e.g., Nesterov, 2018, Chapter 2).”
Dive into Deep Learning (2020, background): “(Nesterov, 2018) has a detailed theoretical discussion in the context of convex optimization.”