Related papers: Global Complexity Analysis of BFGS
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
Reinforcement Learning (RL) algorithms allow artificial agents to improve their action selections so as to increase rewarding experiences in their environments. Deep Reinforcement Learning algorithms require solving a nonconvex and…
Line search methods are a prominent class of iterative methods to solve unconstrained minimization problems. These methods produce new iterates utilizing a suitable step size after determining proper directions for minimization. In this…
The generalized conditional gradient method is a popular algorithm for solving composite problems whose objective function is the sum of a smooth function and a nonsmooth convex function. Many convergence analyses of the algorithm rely on…
In this paper, we consider an accelerated method for solving nonconvex and nonsmooth minimization problems. We propose a Bregman Proximal Gradient algorithm with extrapolation(BPGe). This algorithm extends and accelerates the Bregman…
Recent works have shown that line search methods greatly increase performance of traditional stochastic gradient descent methods on a variety of datasets and architectures [1], [2]. In this work we succeed in extending line search methods…
Variational phase-field models of brittle fracture pose a local constrained minimization problem of a non-convex energy functional. In the discrete setting, the problem is most often solved by alternate minimization, exploiting the separate…
Since the late 1950's when quasi-Newton methods first appeared, they have become one of the most widely used and efficient algorithmic paradigms for unconstrained optimization. Despite their immense practical success, there is little theory…
In this paper we develop accelerated first-order methods for convex optimization with locally Lipschitz continuous gradient (LLCG), which is beyond the well-studied class of convex optimization with Lipschitz continuous gradient. In…
Let $\FF$ be a set of real-valued functions on a set $\XX$ and let $S:\FF \to \GG$ be an arbitrary mapping. We consider the problem of making inference about $S(f)$, with $f\in\FF$ unknown, from a finite set of pointwise evaluations of $f$.…
Motivated by Ridgway's proof of the perceptron algorithm, we study a simple subgradient method for convex inequality systems in Hilbert space. Assuming strict feasibility and bounded subgradients, we establish finite termination for several…
This paper deals with the minimization of large sum of convex functions by Inexact Newton (IN) methods employing subsampled functions, gradients and Hessian approximations. The Conjugate Gradient method is used to compute the inexact Newton…
The optimistic gradient method has seen increasing popularity for solving convex-concave saddle point problems. To analyze its iteration complexity, a recent work [arXiv:1906.01115] proposed an interesting perspective that interprets this…
Many practical optimization problems involve objective function values that are corrupted by unavoidable numerical errors. In smooth nonconvex optimization, quasi-Newton methods combined with line search are widely used due to their…
We introduce Bella, a locally superlinearly convergent Bregman forward backward splitting method for minimizing the sum of two nonconvex functions, one of which satisfying a relative smoothness condition and the other one possibly…
The paper presents a new descent algorithm for locally Lipschitz continuous functions $f:X\to\mathbb{R}$. The selection of a descent direction at some iteration point $x$ combines an approximation of the set-valued gradient of $f$ on a…
In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new…
Non-asymptotic analysis of quasi-Newton methods have gained traction recently. In particular, several works have established a non-asymptotic superlinear rate of $\mathcal{O}((1/\sqrt{t})^t)$ for the (classic) BFGS method by exploiting the…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
This work presents a universal accelerated first-order primal-dual method for affinely constrained convex optimization problems. It can handle both Lipschitz and H\"{o}lder gradients but does not need to know the smoothness level of the…