相关论文: Extragradient Method for $(L_0, L_1)$-Lipschitz Ro…

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…

Goldstein's 1977 idealized iteration for minimizing a Lipschitz objective fixes a distance - the step size - and relies on a certain approximate subgradient. That "Goldstein subgradient" is the shortest convex combination of objective…

We attempt to provide an algorithm for approximating a solution of the quasiconvex equilibrium problem that was proved to exist by K. Fan 1972. The proposed algorithm is an iterative procedure, where the search direction at each iteration…

We consider the well-studied setting of minimizing a convex Lipschitz function using either gradient descent (GD) or its stochastic variant (SGD), and examine the last iterate convergence. By now, it is known that standard stepsize choices…

A practical and efficient scheme for the higher order integration of the Landau-Lifschitz-Gilbert (LLG) equation is presented. The method is based on extrapolation of the two-step explicit midpoint rule and incorporates adaptive time step…

The Extreme Learning Machine (ELM) technique is a machine learning approach for constructing feed-forward neural networks with a single hidden layer and their models. The ELM model can be constructed while being trained by concurrently…

In this paper we study the pseudomonotone equilibrium problem. We consider a new inertial condition for the subgradient extragradient method with self-adaptive step size for approximating a solution of the equilibrium problem in a real…

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…

In this paper, we study a class of misspecified variational inequalities (VIs) where both the monotone operator and nonlinear convex constraints depend on an unknown parameter learned via a secondary VI. Existing data-driven VI methods…

Empirical Risk Minimization (ERM) is a standard technique in machine learning, where a model is selected by minimizing a loss function over constraint set. When the training dataset consists of private information, it is natural to use a…

We study the extragradient method for solving vector quasi-equilibrium problems in Banach spaces, which generalizes the extragradient method for vector equilibrium problems and scalar quasi-equilibrium problems. We propose a regularization…

Variational Inequality (VI) problems have attracted great interest in the machine learning (ML) community due to their application in adversarial and multi-agent training. Despite its relevance in ML, the oft-used strong-monotonicity and…

The gradient method for minimize a differentiable convex function on Riemannian manifolds with lower bounded sectional curvature is analyzed in this paper. The analysis of the method is presented with three different finite procedures for…

Recently, there has been growing interest in developing optimization methods for solving large-scale machine learning problems. Most of these problems boil down to the problem of minimizing an average of a finite set of smooth and strongly…

This paper presents an extension of stochastic gradient descent for the minimization of Lipschitz continuous loss functions. Our motivation is for use in non-smooth non-convex stochastic optimization problems, which are frequently…

We consider monotone variational inequality (VI) problems in multi-GPU settings where multiple processors/workers/clients have access to local stochastic dual vectors. This setting includes a broad range of important problems from…

In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…

We present a new algorithm to solve min-max or min-min problems out of the convex world. We use rigidity assumptions, ubiquitous in learning, making our method applicable to many optimization problems. Our approach takes advantage of hidden…

For first-order smooth optimization, the research on the acceleration phenomenon has a long-time history. Until recently, the mechanism leading to acceleration was not successfully uncovered by the gradient correction term and its…

Adaptive Gradient Descent with Energy (AEGD) is a variant of gradient descent (GD) designed to mitigate step-size sensitivity through an energy-based formulation. AEGD is notable for its unconditional energy stability, which guarantees…