相关论文: A modified subgradient extragradient method for so…

The subgradient method is a classical and foundational approach in non-smooth convex optimization; its simplicity, robustness, and role as a conceptual and algorithmic starting point have made it the backbone of many significant…

This paper is concerned with the variational inequality problem (VIP) over the fixed point set of a quasi-nonexpansive operator. We propose, in particular, an algorithm which entails, at each step, projecting onto a suitably chosen…

In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. To…

In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in…

Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these…

Despite the rise to fame of incremental variance-reduced methods in recent years, their use in nonsmooth optimization is still limited to few simple cases. This is due to the fact that existing methods require to evaluate the proximity…

We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…

This paper considers a generic convex minimization template with affine constraints over a compact domain, which covers key semidefinite programming applications. The existing conditional gradient methods either do not apply to our template…

We develop an interior-point approach to solve constrained variational inequality (cVI) problems. Inspired by the efficacy of the alternating direction method of multipliers (ADMM) method in the single-objective context, we generalize ADMM…

We propose a subgradient-based method for finding the maximum feasible subsystem in a collection of closed sets with respect to a given closed set $C$ (MFS$_C$). In this method, we reformulate the MFS$_C$ problem as an $\ell_0$ optimization…

In this paper we present a variant of the proximal forward-backward splitting iteration for solving nonsmooth optimization problems in Hilbert spaces, when the objective function is the sum of two nondifferentiable convex functions. The…

We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…

This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a…

This work introduces a moving anchor acceleration technique to extragradient algorithms for smooth structured minimax problems. The moving anchor is introduced as a generalization of the original algorithmic anchoring framework, i.e. the…

Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…

In this paper, we design and analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) stochastic optimization problems. Adaptive methods that use exponential moving averages…

Classical extragradient schemes and their stochastic counterpart represent a cornerstone for resolving monotone variational inequality problems. Yet, such schemes have a per-iteration complexity of two projections onto a convex set and…

We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general…

This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…

The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…