相关论文: Self-concordant smoothing in proximal quasi-Newton…
A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of…
We propose a novel stochastic smoothing accelerated gradient (SSAG) method for general constrained nonsmooth convex composite optimization, and analyze the convergence rates. The SSAG method allows various smoothing techniques, and can deal…
The present work investigates the segmentation of textures by formulating it as a strongly convex optimization problem, aiming to favor piecewise constancy of fractal features (local variance and local regularity) widely used to model…
For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…
In this paper, we address stochastic optimization problems involving a composition of a non-smooth outer function and a smooth inner function, a formulation frequently encountered in machine learning and operations research. To deal with…
We consider the setting where the nodes of an undirected, connected network collaborate to solve a shared objective modeled as the sum of smooth functions. We assume that each summand is privately known by a unique node. NEAR-DGD is a…
Minimax problems have gained tremendous attentions across the optimization and machine learning community recently. In this paper, we introduce a new quasi-Newton method for minimax problems, which we call $J$-symmetric quasi-Newton method.…
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…
This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…
We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…
Many machine learning techniques sacrifice convenient computational structures to gain estimation robustness and modeling flexibility. However, by exploring the modeling structures, we find these "sacrifices" do not always require more…
The graduated optimization approach is a method for finding global optimal solutions for nonconvex functions by using a function smoothing operation with stochastic noise. This paper makes three contributions regarding graduated…
In this paper, we devise a $\operatorname{prox}$-based semi-smooth Newton method for the non-differentiable TV-minimization problem. To this end, the primal-dual optimality conditions are reformulated as a nonlinear operator equation with…
This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees and practical performance. The method contains elements of two existing methods: the…
We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…
We develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm incorporates a variance reduction mechanism and the resulting…
We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the…
Algorithms for solving nonconvex, nonsmooth, finite-sum optimization problems are proposed and tested. In particular, the algorithms are proposed and tested in the context of an optimization problem formulation arising in semi-supervised…
In this paper, we propose objective-function-free (OFF) variants of the proximal Newton method for nonconvex composite optimization problems and the regularized Newton method for unconstrained optimization problems, respectively, using…
Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…