Related papers: A non-monotone trust-region method with noisy orac…
In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only noisy gradient and…
We introduce biased gradient oracles to capture a setting where the function measurements have an estimation error that can be controlled through a batch size parameter. Our proposed oracles are appealing in several practical contexts, for…
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 work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…
A trust-region algorithm using inexact function and derivatives values is introduced for solving unconstrained smooth optimization problems. This algorithm uses high-order Taylor models and allows the search of strong approximate minimizers…
We introduce a two-level trust-region method (TLTR) for solving unconstrained nonlinear optimization problems. Our method uses a composite iteration step, which is based on two distinct search directions. The first search direction is…
In this paper, we propose a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while…
The difficulty of minimizing a nonconvex function is in part explained by the presence of saddle points. This slows down optimization algorithms and impacts worst-case complexity guarantees. However, many nonconvex problems of interest…
We target the problem of finding a local minimum in non-convex finite-sum minimization. Towards this goal, we first prove that the trust region method with inexact gradient and Hessian estimation can achieve a convergence rate of order…
While first-order optimization methods such as stochastic gradient descent (SGD) are popular in machine learning (ML), they come with well-known deficiencies, including relatively-slow convergence, sensitivity to the settings of…
We propose a nonsmooth trust-region method for solving optimization problems with locally Lipschitz continuous functions, with application to problems constrained by variational inequalities of the second kind. Under suitable assumptions on…
The first-order optimality condition of convexly constrained nonconvex nonconcave min-max optimization problems with box constraints formulates a nonmonotone variational inequality (VI), which is equivalent to a system of nonsmooth…
Motivated by TRACE algorithm [Curtis et al. 2017], we propose a trust region algorithm for finding second order stationary points of a linearly constrained non-convex optimization problem. We show the convergence of the proposed algorithm…
In recent years, random subspace methods have been actively studied for large-dimensional nonconvex problems. Recent subspace methods have improved theoretical guarantees such as iteration complexity and local convergence rate while…
In recent years, we have witnessed the emergence of scientific machine learning as a data-driven tool for the analysis, by means of deep-learning techniques, of data produced by computational science and engineering applications. At the…
We develop a trust-region method for minimizing the sum of a smooth term $f$ and a nonsmooth term $h$), both of which can be nonconvex. Each iteration of our method minimizes a possibly nonconvex model of $f + h$ in a trust region. The…
In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…
Non-monotone trust-region methods are known to provide additional benefits for scalar and multi-objective optimization, such as enhancing the probability of convergence and improving the speed of convergence. For optimization of set-valued…
Physics-informed machine learning and inverse modeling require the solution of ill-conditioned non-convex optimization problems. First-order methods, such as SGD and ADAM, and quasi-Newton methods, such as BFGS and L-BFGS, have been applied…
We investigate a trust-region algorithm to solve a nonconvex optimization problem with $L^p$-regularization for $p\in(0,1)$. The algorithm relies on descent properties of a so-called generalized Cauchy point that can be obtained efficiently…