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This paper is devoted to the study of acceleration methods for an inequality constrained convex optimization problem by using Lyapunov functions. We first approximate such a problem as an unconstrained optimization problem by employing the…
This work is concerned with the optimization of nonconvex, nonsmooth composite optimization problems, whose objective is a composition of a nonlinear mapping and a nonsmooth nonconvex function, that can be written as an infimal convolution…
Level-set optimization formulations with data-driven constraints minimize a regularization functional subject to matching observations to a given error level. These formulations are widely used, particularly for matrix completion and…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
This paper proposes a new inexact manifold proximal linear (IManPL) algorithm for solving nonsmooth, nonconvex composite optimization problems over an embedded submanifold. At each iteration, IManPL solves a convex subproblem inexactly,…
As a technique to alleviate the pressure of data annotation, semi-supervised learning (SSL) has attracted widespread attention. In the specific domain of medical image segmentation, semi-supervised methods (SSMIS) have become a research…
This paper presents a pseudo-spectral method for Dynamic Optimization Problems (DOPs) that allows for tight polynomial bounds to be achieved via flexible sub-intervals. The proposed method not only rigorously enforces inequality…
We propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications. Our optimization algorithms feature optimal convergence guarantees under a variety of common structure assumptions…
In this paper, we propose a new method based on the Sliding Algorithm from Lan(2016, 2019) for the convex composite optimization problem that includes two terms: smooth one and non-smooth one. Our method uses the stochastic noised…
Recent work by Woodworth et al. (2020) shows that the optimization dynamics of gradient descent for overparameterized problems can be viewed as low-dimensional dual dynamics induced by a mirror map, explaining the implicit regularization…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
This paper presents a density-based topology optimization approach considering additive manufacturing limitations. The presented method considers the minimum size of parts, the minimum size of cavities, the inability of printing overhanging…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
We investigate different randomizations for mirror descent method. We try to propose such a randomization that allows us to use sparsity of the problem as much as it possible. In the paper one can also find a generalization of randomizaed…
In this paper we consider iterative methods for stochastic variational inequalities (s.v.i.) with monotone operators. Our basic assumption is that the operator possesses both smooth and nonsmooth components. Further, only noisy observations…
We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…
Recent advances (Sherman, 2017; Sidford and Tian, 2018; Cohen et al., 2021) have overcome the fundamental barrier of dimension dependence in the iteration complexity of solving $\ell_\infty$ regression with first-order methods. Yet it…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
The constrained minimization (respectively maximization) of directed distances and of related generalized entropies is a fundamental task in information theory as well as in the adjacent fields of statistics, machine learning, artificial…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…