Related papers: On proximal gradient mapping and its minimization …
This paper proposes a new family of algorithms for the online optimisation of composite objectives. The algorithms can be interpreted as the combination of the exponentiated gradient and $p$-norm algorithm. Combined with algorithmic ideas…
In this article we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since…
We first propose a decentralized proximal stochastic gradient tracking method (DProxSGT) for nonconvex stochastic composite problems, with data heterogeneously distributed on multiple workers in a decentralized connected network. To save…
This paper presents a unified analysis for the proximal subgradient method (Prox-SubGrad) type approach to minimize an overall objective of $f(x)+r(x)$, subject to convex constraints, where both $f$ and $r$ are weakly convex, nonsmooth, and…
Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…
Motivated by conforming finite element methods for elliptic problems of second order, we analyze the approximation of the gradient of a target function by continuous piecewise polynomial functions over a simplicial mesh. The main result is…
This paper proposes an accelerated proximal point method for maximally monotone operators. The proof is computer-assisted via the performance estimation problem approach. The proximal point method includes various well-known convex…
Accelerated proximal gradient methods have recently been developed for solving quasi-static incremental problems of elastoplastic analysis with some different yield criteria. It has been demonstrated through numerical experiments that these…
This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…
The purpose of this paper is to introduce two new classes of accelerated distributed proximal conjugate gradient algorithms for multi-agent constrained optimization problems; given as minimization of a function decomposed as a sum of M…
In this paper we consider large-scale composite nonconvex optimization problems having the objective function formed as a sum of three terms, first has block coordinate-wise Lipschitz continuous gradient, second is twice differentiable but…
In many modern machine learning applications, structures of underlying mathematical models often yield nonconvex optimization problems. Due to the intractability of nonconvexity, there is a rising need to develop efficient methods for…
The proximal point method (PPM) is a fundamental method in optimization that is often used as a building block for designing optimization algorithms. In this work, we use the PPM method to provide conceptually simple derivations along with…
Mini-batch gradient descent based methods are the de facto algorithms for training neural network architectures today. We introduce a mini-batch selection strategy based on submodular function maximization. Our novel submodular formulation…
In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…
We introduce a proximal version of the stochastic dual coordinate ascent method and show how to accelerate the method using an inner-outer iteration procedure. We analyze the runtime of the framework and obtain rates that improve…
We study the convergence rate of the proximal-gradient homotopy algorithm applied to norm-regularized linear least squares problems, for a general class of norms. The homotopy algorithm reduces the regularization parameter in a series of…
Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…
This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…