相关论文: Nonsmooth trust-region algorithm with applications…
We study the oracle complexity of nonsmooth nonconvex optimization, with the algorithm assumed to have access only to local function information. It has been shown by Davis, Drusvyatskiy, and Jiang (2023) that for nonsmooth Lipschitz…
We propose a derivative-free trust-region method based on finite-difference gradient approximations for smooth optimization problems with convex constraints. The proposed method does not require computing an approximate stationarity…
This paper addresses some trust-region methods equipped with nonmonotone strategies for solving nonlinear unconstrained optimization problems. More specifically, the importance of using nonmonotone techniques in nonlinear optimization is…
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, a globally convergent trust region proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
A novel trust region method for solving linearly constrained nonlinear programs is presented. The proposed technique is amenable to a distributed implementation, as its salient ingredient is an alternating projected gradient sweep in place…
An algorithm is proposed for solving stochastic and finite sum minimization problems. Based on a trust region methodology, the algorithm employs normalized steps, at least as long as the norms of the stochastic gradient estimates are within…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…
In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…
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…
We consider unconstrained multi-criteria optimization problems with finite sum objective functions. The proposed algorithm belongs to a non-monotone trust region framework where additional sampling approach is used to govern the sample size…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
Adaptive trust-region methods attempt to maintain strong convergence guarantees without depending on conservative estimates of problem properties such as Lipschitz constants. However, on close inspection, one can show existing adaptive…
The Proximal Point Method (PPM) (Rockafellar, 1976) is a fundamental tool for nonsmooth convex optimization. However, its convergence is not linear under general convexity in the absence of strong convexity or other structural assumptions.…
We propose a single time-scale stochastic subgradient method for constrained optimization of a composition of several nonsmooth and nonconvex functions. The functions are assumed to be locally Lipschitz and differentiable in a generalized…
In this work, we introduce a novel stochastic second-order method, within the framework of a non-monotone trust-region approach, for solving the unconstrained, nonlinear, and non-convex optimization problems arising in the training of deep…
We study unconstrained optimization problems of nonsmooth, nonconvex Lipschitz functions, using only noisy pairwise comparisons governed by a known link function. Our goal is to compute a $(\delta,\varepsilon)$-Goldstein stationary point.…
A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method…
In this work we present TRFD, a derivative-free trust-region method based on finite differences for minimizing composite functions of the form $f(x)=h(F(x))$, where $F$ is a black-box function assumed to have a Lipschitz continuous…