Many problems in data science (e.g. machine learning, optimization and statistics) can be cast as loss minimization problems of the form min x∈Rd f(x), where f(x) = 1 n n∑ i=1 fi(x). (P) We assume that each individual function fi: Rd → R is convex and has Lipschitz continuous partial gradients with constants {Lij}j. That is, ‖∇jfi(x)−∇jfi(y) ‖ ≤ Lij‖x − y‖, ∀x, y ∈ Rd. Further we assume that f: Rd → R is µ-strongly convex: f(y) ≥ f(x) + 〈∇f(x), y − x〉+
We give a derivation of the result for the rate of linear convergence in p. 4 of the paper. Consider...
We extend the previous analysis of Schmidt et al. [2011] to derive the linear convergence rate obtai...
The Frank-Wolfe method (a.k.a. conditional gradient algorithm) for smooth optimization has regained ...
x∈Q f (x), where Q ⊆ Rn is a closed convex set. Def: For > 0, find x ̄ ∈ Q satisfying f (x̄) ≤ ...
Abstract. We modify Nesterov’s constant step gradient method for strongly convex functions with Lips...
We follow the proof of [1] to derive bounds. We highlight the fact that since the loss function H is...
The convergence behavior of gradient methods for minimizing convex differentiable functions is one o...
Motivated by recent work of Renegar, we present new computational methods and associated computation...
Wolfe’s universal algorithm www.di.ens.fr/~fbach/wolfe_anonymous.pdf Conditional gradients everywher...
(2005). Notice also that minimization of f is the same as maximization of −f, so there is no need to...
This note discusses proofs for convergence of first-order methods based on simple potential-function...
We describe a steepest-descent potential reduction method for linear and convex minimization over a ...
Last time: numerical linear algebra primer In Rn, rough flop counts for basic operations are as foll...
This dissertation is concerned with the following optimization problem: P[subscript o]: min H[p(x), ...
Convex optimization, the study of minimizing convex functions over convex sets, is host to a multit...
We give a derivation of the result for the rate of linear convergence in p. 4 of the paper. Consider...
We extend the previous analysis of Schmidt et al. [2011] to derive the linear convergence rate obtai...
The Frank-Wolfe method (a.k.a. conditional gradient algorithm) for smooth optimization has regained ...
x∈Q f (x), where Q ⊆ Rn is a closed convex set. Def: For > 0, find x ̄ ∈ Q satisfying f (x̄) ≤ ...
Abstract. We modify Nesterov’s constant step gradient method for strongly convex functions with Lips...
We follow the proof of [1] to derive bounds. We highlight the fact that since the loss function H is...
The convergence behavior of gradient methods for minimizing convex differentiable functions is one o...
Motivated by recent work of Renegar, we present new computational methods and associated computation...
Wolfe’s universal algorithm www.di.ens.fr/~fbach/wolfe_anonymous.pdf Conditional gradients everywher...
(2005). Notice also that minimization of f is the same as maximization of −f, so there is no need to...
This note discusses proofs for convergence of first-order methods based on simple potential-function...
We describe a steepest-descent potential reduction method for linear and convex minimization over a ...
Last time: numerical linear algebra primer In Rn, rough flop counts for basic operations are as foll...
This dissertation is concerned with the following optimization problem: P[subscript o]: min H[p(x), ...
Convex optimization, the study of minimizing convex functions over convex sets, is host to a multit...
We give a derivation of the result for the rate of linear convergence in p. 4 of the paper. Consider...
We extend the previous analysis of Schmidt et al. [2011] to derive the linear convergence rate obtai...
The Frank-Wolfe method (a.k.a. conditional gradient algorithm) for smooth optimization has regained ...