Related papers: MOCCA: mirrored convex/concave optimization for no…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
Here we study non-convex composite optimization: first, a finite-sum of smooth but non-convex functions, and second, a general function that admits a simple proximal mapping. Most research on stochastic methods for composite optimization…
Optimizing non-convex functions is a fundamental challenge across machine learning and combinatorial optimization. We introduce and study $\gamma$-weakly $\theta$-up-concavity, a novel first-order condition that characterizes a broad class…
This paper considers the problem of minimizing an expectation function over a closed convex set, coupled with a {\color{black} functional or expectation} constraint on either decision variables or problem parameters. We first present a new…
We revisit the classical dual ascent algorithm for minimization of convex functionals in the presence of linear constraints, and give convergence results which apply even for non-convex functionals. We describe limit points in terms of the…
We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general scheme we propose nearly optimal methods for minimizing…
The minimax problems arise throughout machine learning applications, ranging from adversarial training and policy evaluation in reinforcement learning to AUROC maximization. To address the large-scale data challenges across multiple clients…
The paper is devoted to new modifications of recently proposed adaptive methods of Mirror Descent for convex minimization problems in the case of several convex functional constraints. Methods for problems of two classes are considered. The…
This paper presents two inexact composite gradient methods, one inner accelerated and another doubly accelerated, for solving a class of nonconvex spectral composite optimization problems. More specifically, the objective function for these…
The paper deals with stochastic difference-of-convex functions (DC) programs, that is, optimization problems whose the cost function is a sum of a lower semicontinuous DC function and the expectation of a stochastic DC function with respect…
Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization…
In this paper, we develop a novel distributed algorithm for addressing convex optimization with both nonlinear inequality and linear equality constraints, where the objective function can be a general nonsmooth convex function and all the…
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…
This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural…
We study composite optimization problems in which the smooth part of the objective function is \( p \)-times continuously differentiable, where \( p \geq 1 \) is an integer. Higher-order methods are known to be effective for solving such…
We propose a proximal variable smoothing algorithm for nonsmooth optimization problem with sum of three functions involving weakly convex composite function. The proposed algorithm is designed as a time-varying forward-backward splitting…
Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank…
We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using…
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…
Machine learning problems with multiple objective functions appear either in learning with multiple criteria where learning has to make a trade-off between multiple performance metrics such as fairness, safety and accuracy; or, in…