Related papers: A general framework for inexact splitting algorith…
We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in \cite{vu} for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators…
We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…
Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…
We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…
This paper presents a novel restarted version of Nesterov's accelerated gradient method and establishes its optimal iteration-complexity for solving convex smooth composite optimization problems. The proposed restart accelerated gradient…
We provide a framework for computing the exact worst-case performance of any algorithm belonging to a broad class of oracle-based first-order methods for composite convex optimization, including those performing explicit, projected,…
This paper provides a theoretical and numerical comparison of classical first-order splitting methods for solving smooth convex optimization problems and cocoercive equations. From a theoretical point of view, we compare convergence rates…
In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators.…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…
Physics-informed neural networks (PINNs) have recently emerged as a popular approach for solving forward and inverse problems involving partial differential equations (PDEs). Compared to fully connected neural networks, PINNs based on…
In this paper, we propose an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale structured convex optimization problems. Unlike the exact versions considered in literature,…
Hyperparameter optimization (HPO) is crucial for strong performance of deep learning algorithms and real-world applications often impose some constraints, such as memory usage, or latency on top of the performance requirement. In this work,…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
Efficient numerical solvers for partial differential equations empower science and engineering. One of the commonly employed numerical solvers is the preconditioned conjugate gradient (PCG) algorithm which can solve large systems to a given…
The Primal-Dual hybrid gradient (PDHG) method is a powerful optimization scheme that breaks complex problems into simple sub-steps. Unfortunately, PDHG methods require the user to choose stepsize parameters, and the speed of convergence is…
In this work we propose a new splitting technique, namely Asymmetric Forward-Backward-Adjoint splitting, for solving monotone inclusions involving three terms, a maximally monotone, a cocoercive and a bounded linear operator. Classical…
Optimization is at the heart of machine learning, statistics and many applied scientific disciplines. It also has a long history in physics, ranging from the minimal action principle to finding ground states of disordered systems such as…
The breakthrough ideas in the modern proximal splitting methodologies allow us to express the set of all minimizers of a superposition of multiple nonsmooth convex functions as the fixed point set of computable nonexpansive operators. In…
We investigate the convergence properties of a stochastic primal-dual splitting algorithm for solving structured monotone inclusions involving the sum of a cocoercive operator and a composite monotone operator. The proposed method is the…