相关论文: Fast inertial dynamics and FISTA algorithms in con…

We consider the minimization of a convex objective function subject to the set of minima of another convex function, under the assumption that both functions are twice continuously differentiable. We approach this optimization problem from…

This paper is devoted to the investigation of inertial dynamical systems with implicit Hessian-driven damping for strongly quasiconvex optimization which is a specific class of nonconvex optimization problems. We first establish exponential…

In a separable Hilbert space, we study the minimization problem of a convex smooth function with Lipschitz continuous gradient whose evaluations are corrupted by random noise. To this end, we associate a stochastic inertial system that…

In a Hilbert setting we aim to study a second order in time differential equation, combining viscous and Hessian-driven damping, containing a time scaling parameter function and a Tikhonov regularization term. The dynamical system is…

In this paper, we revisit the class of iterative shrinkage-thresholding algorithms (ISTA) for solving the linear inverse problem with sparse representation, which arises in signal and image processing. It is shown in the numerical…

We obtain new quantitative estimates of the vanishing viscosity approximation for time-dependent, degenerate, Hamilton-Jacobi equations that are neither concave nor convex in the gradient and Hessian entries of the form $\partial_t…

For first-order smooth optimization, the research on the acceleration phenomenon has a long-time history. Until recently, the mechanism leading to acceleration was not successfully uncovered by the gradient correction term and its…

Very recently, the papers "Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proof" by Jang and Ryu, and "The Iterates of Nesterov's Accelerated Algorithm Converge in the Critical Regimes" by Bot, Fadili, and…

In this paper we propose new numerical algorithms in the setting of unconstrained optimization problems and we study the rate of convergence in the iterates of the objective function. Furthermore, our algorithms are based upon splitting and…

In this paper, we first study nonsmooth steepest descent method for nonsmooth functions defined on Hilbert space and establish the corresponding algorithm by proximal subgradients. Then, we use this algorithm to find stationary points for…

In this paper, we conduct a theoretical and numerical study of the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) under strong convexity assumptions. We propose an autonomous Lyapunov function that reflects the strong convexity of…

This paper is concerned with convex composite minimization problems in a Hilbert space. In these problems, the objective is the sum of two closed, proper, and convex functions where one is smooth and the other admits a computationally…

In this work, we approach the problem of finding the zeros of a continuous and monotone operator through a second-order dynamical system with a damping term of the form $1/t^{r}$, where $r\in [0, 1]$. The system features the time derivative…

In this work, we approach the minimization of a continuously differentiable convex function under linear equality constraints by a second-order dynamical system with asymptotically vanishing damping term. The system is formulated in terms…

Second-order dynamical systems are important tools for solving optimization problems, and most of existing works in this field have focused on unconstrained optimization problems. In this paper, we propose an inertial primal-dual dynamical…

The "Inertial Forward-Backward algorithm" (IFB) is a powerful tool for convex nonsmooth minimization problems, it gives the well known "fast iterative shrinkage-thresholding algorithm " (FISTA), which enjoys $O\left( {\frac{1}{{{k^2}}}}…

In convex optimization, first-order optimization methods efficiently minimizing function values have been a central subject study since Nesterov's seminal work of 1983. Recently, however, Kim and Fessler's OGM-G and Lee et al.'s FISTA-G…

In this paper, in the setting of Hilbert spaces, we consider a Tikhonov regularized second-order plus first-order primal-dual dynamical system with asymptotically vanishing damping for a linear equality constrained convex optimization…

In a real Hilbert space $\mathcal{H}$. Given any function $f$ convex differentiable whose solution set $\argmin_{\mathcal{H}}\,f$ is nonempty, by considering the Proximal Algorithm $x_{k+1}=\text{prox}_{\b_k f}(d x_k)$, where $0<d<1$ and…

A problem of great interest in optimization is to minimize a sum of two closed, proper, and convex functions where one is smooth and the other has a computationally inexpensive proximal operator. In this paper we analyze a family of…