相关论文: Generalized-Hukuhara-Gradient Efficient-Direction …
We propose a hybridizable discontinuous Galerkin (HDG) method combined with convex-concave splitting for the temporal discretization of the convective Cahn-Hilliard equation. The convection term is discretized explicitly without…
In this work, we focus on the study of stochastic zeroth-order (ZO) optimization which does not require first-order gradient information and uses only function evaluations. The problem of ZO optimization has emerged in many recent machine…
This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…
Making the gradients small is a fundamental optimization problem that has eluded unifying and simple convergence arguments in first-order optimization, so far primarily reserved for other convergence criteria, such as reducing the…
Many problems in robotics, such as estimating the state from noisy sensor data or aligning two point clouds, can be posed and solved as least-squares problems. Unfortunately, vanilla nonminimal solvers for least-squares problems are…
We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
In this paper, we combine the positive aspects of the Gradient Sampling (GS) and bundle methods, as the most efficient methods in nonsmooth optimization, to develop a robust method for solving unconstrained nonsmooth convex optimization…
Communication has been seen as a significant bottleneck in industrial applications over large-scale networks. To alleviate the communication burden, sign-based optimization algorithms have gained popularity recently in both industrial and…
We consider the problem of minimizing a convex function that depends on an uncertain parameter $\theta$. The uncertainty in the objective function means that the optimum, $x^*(\theta)$, is also a function of $\theta$. We propose an…
In this paper we present a variant of the proximal forward-backward splitting iteration for solving nonsmooth optimization problems in Hilbert spaces, when the objective function is the sum of two nondifferentiable convex functions. The…
In this paper, we study a class of fractional optimization problems, in which the numerator of the objective is the sum of a convex function and a differentiable function with a Lipschitz continuous gradient, while the denominator is a…
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…
This paper studies a class of distributed optimization algorithms by a set of agents, where each agent has only access to its own local convex objective function, and jointly minimizes the sum of the functions. The communications among…
There is widespread sentiment that it is not possible to effectively utilize fast gradient methods (e.g. Nesterov's acceleration, conjugate gradient, heavy ball) for the purposes of stochastic optimization due to their instability and error…
Minimizing finite sums of functions is a central problem in optimization, arising in numerous practical applications. Such problems are commonly addressed using first-order optimization methods. However, these procedures cannot be used in…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
In this paper we consider a nonconvex unconstrained optimization problem minimizing a twice differentiable objective function with H\"older continuous Hessian. Specifically, we first propose a Newton-conjugate gradient (Newton-CG) method…
As a foundation for optimization, convexity is useful beyond the classical settings of Euclidean and Hilbert space. The broader arena of nonpositively curved metric spaces, which includes manifolds like hyperbolic space, as well as metric…
Optimization over low rank matrices has broad applications in machine learning. For large scale problems, an attractive heuristic is to factorize the low rank matrix to a product of two much smaller matrices. In this paper, we study the…
We investigate the convergence rate of the recently proposed subgradient-push method for distributed optimization over time-varying directed graphs. The subgradient-push method can be implemented in a distributed way without requiring…