Accelerated Proximal Gradient Methods for Nonconvex Programming

By Huan Li, Zhouchen Lin. Neural Information Processing Systems, 2015

488 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0330d7716fa7cfdbe9d4ddcec55133a7880f8007

How researchers see this paper

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

Citations in the corpus

First-order Stochastic Algorithms for Escaping From Saddle Points in Almost Linear Time (2017, background): “Recently, several studies have explored AG methods for non-convex optimization [15, 19, 3, 12].”
Variance Reduction for Faster Non-Convex Optimization (2016, result): “The recent interesting results of Li and Lin [17] and Ghadimi and Lan [12] unify the theory of non-convex and convex optimization in the following sense.”
A variational perspective on accelerated methods in optimization (2016, background): “Introduced by Nesterov in 1983 [24] in the context of gradient descent, the acceleration idea has been extended to a wide range of other settings, including composite optimization [27, 33, 7], stochastic optimization [12, 18], nonconvex optimization [11, 21], and conic programming [19].”
Accelerated Methods for Non-Convex Optimization (2016, methodology): “(7) Note that the method calls Accelerated-gradient-descent (Line 7) with accuracy parameter ′ = √ γ/(50(L1 + 2γ)); using γ ≤ L1 we may apply Lemma 2.5 to bound the running time of each call by O ( Tgrad ( 1 + √ L1 + 2γ γ log 4(L1 + 2γ) 2∆f γ( ′)2 )) = O ( Tgrad √ L1 γ log ( 2 + L31∆f γ2 2 )) .”
Guaranteed Sufficient Decrease for Stochastic Variance Reduced Gradient Optimization (2018, methodology): “For example, [25] proposed the following sufficient decrease condition:”
Understanding Traffic Density from Large-Scale Web Camera Data (2017, methodology): “x (i) D(B(i) j )) 2 + kWk2 F + jWj 1 s.t. rank(W) r (4) To solve this rank-constrained problem that has a nonsmooth objective function, we develop an accelerated projected subgradient descent (APSD) [20] algorithm outlined in Algorithm1, which iteratively performs subgradient descent, rank projectio”
Meta-Graph Based Recommendation Fusion over Heterogeneous Information Networks (2017, methodology): “Algorithm 2 nmAPG [17] algorithm for (9).”