相关论文: Numerical methods in large-scale optimization: ine…

The paper proposes a linesearch for a primal-dual method. Each iteration of the linesearch requires to update only the dual (or primal) variable. For many problems, in particular for regularized least squares, the linesearch does not…

Gradient-type distributed optimization methods have blossomed into one of the most important tools for solving a minimization learning task over a networked agent system. However, only one gradient update per iteration is difficult to…

In this paper we present a complete iteration complexity analysis of inexact first order Lagrangian and penalty methods for solving cone constrained convex problems that have or may not have optimal Lagrange multipliers that close the…

This paper provides a self-contained ordinary differential equation solver approach for separable convex optimization problems. A novel primal-dual dynamical system with built-in time rescaling factors is introduced, and the exponential…

In this paper, we develop a novel accelerated fixed-point-based framework using delayed inexact oracles to approximate a fixed point of a nonexpansive operator (or equivalently, a root of a co-coercive operator), a central problem in…

In this paper, we study a bilinear saddle point problem of the form $\min_{x}\max_{y} F(x) + \langle Ax, y \rangle - G(y)$, where $F$ and $G$ are $\mu_F$- and $\mu_G$-strongly convex functions, respectively. By incorporating Nesterov…

Offline Reinforcement Learning (RL) aims to learn a near-optimal policy from a fixed dataset of transitions collected by another policy. This problem has attracted a lot of attention recently, but most existing methods with strong…

We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…

This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…

Selecting the fastest algorithm for a specific signal/image processing task is a challenging question. We propose an approach based on the Performance Estimation Problem framework that numerically and automatically computes the worst-case…

Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in…

Incremental gradient and incremental proximal methods are a fundamental class of optimization algorithms used for solving finite sum problems, broadly studied in the literature. Yet, without strong convexity, their convergence guarantees…

First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…

We study structured optimization problems with polynomial objective function and polynomial equality constraints. The structure comes from a multi-grading on the polynomial ring in several variables. For fixed multi-degrees we determine the…

We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…

In this work we consider a possibility to use the conception of $(\delta, L)$-model of a function for optimization tasks, whereby solving a primal problem there is a necessity to recover a solution of a dual problem. The conception of…

Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost. This tutorial highlights a shift in optimization: using differentiable programming not only to execute algorithms but to learn…

The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local…

Decentralized optimization to minimize a finite sum of functions over a network of nodes has been a significant focus within control and signal processing research due to its natural relevance to optimal control and signal estimation…

Zero-order optimization techniques are becoming increasingly popular in robotics due to their ability to handle non-differentiable functions and escape local minima. These advantages make them particularly useful for trajectory optimization…