相关论文: On Equivalence between Optimality Criteria and Pro…

We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…

We study the so-called distributed two-time-scale gradient method for solving convex optimization problems over a network of agents when the communication bandwidth between the nodes is limited, and so information that is exchanged between…

Quasi-convex optimization acts a pivotal part in many fields including economics and finance; the subgradient method is an effective iterative algorithm for solving large-scale quasi-convex optimization problems. In this paper, we…

Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…

It is well known that there have been many numerical algorithms for solving nonsmooth minimax problems, numerical algorithms for nonsmooth minimax problems with joint linear constraints are very rare. This paper aims to discuss optimality…

We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…

Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient…

We study the optimization of the expected long-term reward in finite partially observable Markov decision processes over the set of stationary stochastic policies. In the case of deterministic observations, also known as state aggregation,…

Smoothing accelerated gradient methods achieve faster convergence rates than that of the subgradient method for some nonsmooth convex optimization problems. However, Nesterov's extrapolation may require gradients at infeasible points, and…

We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of…

We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…

In this paper, it was proposed a new concept of the inexact higher degree $(\delta, L, q)$-model of a function that is a generalization of the inexact $(\delta, L)$-model, $(\delta, L)$-oracle and $(\delta, L)$-oracle of degree $q \in…

We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity…

We introduce a new form of Lagrangian and propose a simple first-order algorithm for nonconvex optimization with nonlinear equality constraints. We show the algorithm generates bounded dual iterates, and establish the convergence to KKT…

Motivated by some applications in signal processing and machine learning, we consider two convex optimization problems where, given a cone $K$, a norm $\|\cdot\|$ and a smooth convex function $f$, we want either 1) to minimize the norm over…

In this paper, we study the standard formulation of an optimization problem when the computation of gradient is not available. Such a problem can be classified as a "black box" optimization problem, since the oracle returns only the value…

We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal…

Augmented Lagrangian and optimistic primal--dual methods stabilize equality-constrained optimization through seemingly different mechanisms: the former adds constraint-dependent primal curvature, while the latter adds dual memory. Recent…

Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…

The need for fast and robust optimization algorithms are of critical importance in all areas of machine learning. This paper treats the task of designing optimization algorithms as an optimal control problem. Using regret as a metric for an…