Related papers: A non-smooth trust-region method for locally Lipsc…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang and the…
We consider a composite optimization problem where the sum of a continuously differentiable and a merely lower semicontinuous function has to be minimized. The proximal gradient algorithm is the classical method for solving such a problem…
Historically speaking, it is hard to balance the global and local efficiency of second-order optimization algorithms. For instance, the classical Newton's method possesses excellent local convergence but lacks global guarantees, often…
This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized…
In this paper, we employ Tseng's extragradient method with the self-adaptive stepsize to solve variational inequality problems involving non-Lipschitz continuous and quasimonotone operators in real Hilbert spaces. The convergence of the…
In terms of layer potential methods, this paper is devoted to study the $L^2$ boundary value problems for nonhomogeneous elliptic operators with rapidly oscillating coefficients in a periodic setting. Under a low regularity assumption on…
In this paper, we provide a generalization of the forward-backward splitting algorithm for minimizing the sum of a proper convex lower semicontinuous function and a differentiable convex function whose gradient satisfies a locally…
Coordinate-type subgradient methods for addressing nonsmooth optimization problems are relatively underexplored due to the set-valued nature of the subdifferential. In this work, our study focuses on nonsmooth composite optimization…
We propose a trust-region stochastic sequential quadratic programming algorithm (TR-StoSQP) to solve nonlinear optimization problems with stochastic objectives and deterministic equality constraints. We consider a fully stochastic setting,…
In this paper, we develop and analyze sub-sampled trust-region methods for solving finite-sum optimization problems. These methods employ subsampling strategies to approximate the gradient and Hessian of the objective function,…
This paper considers decentralized nonsmooth nonconvex optimization problem with Lipschitz continuous local functions. We propose an efficient stochastic first-order method with client sampling, achieving the $(\delta,\epsilon)$-Goldstein…
We study the Inexact Restoration framework with random models for minimizing functions whose evaluation is subject to errors. We propose a constrained formulation that includes well-known stochastic problems and an algorithm applicable when…
Constrained optimization in high-dimensional black-box settings is difficult due to expensive evaluations, the lack of gradient information, and complex feasibility regions. In this work, we propose a Bayesian optimization method that…
Profile likelihood confidence intervals are a robust alternative to Wald's method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood…
This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…
We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex. Compositions of Lipschitz convex functions with smooth maps are the primary examples of such…
Distributed optimization plays an important role in modern large-scale machine learning and data processing systems by optimizing the utilization of computational resources. One of the classical and popular approaches is Local Stochastic…
Constrained optimization problems where both the objective and constraints may be nonsmooth and nonconvex arise across many learning and data science settings. In this paper, we show for any Lipschitz, weakly convex objectives and…
We propose a novel algorithm, TR-SVR, for solving unconstrained stochastic optimization problems. This method builds on the trust-region framework, which effectively balances local and global exploration in optimization tasks. TR-SVR…