Related papers: An inertial extrapolation method for convex simple…

In this paper we propose a subgradient algorithm for solving the equilibrium problem where the bifunction may be quasiconvex with respect to the second variable. The convergence of the algorithm is investigated. A numerical example for a…

Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics,…

The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…

This note studies numerical methods for solving compositional optimization problems, where the inner function is smooth, and the outer function is Lipschitz continuous, non-smooth, and non-convex but exhibits one of two special structures…

Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…

An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…

This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…

This paper considers a networked system with a finite number of users and supposes that each user tries to minimize its own private objective function over its own private constraint set. It is assumed that each user's constraint set can be…

Bilevel optimisation is used in inverse imaging problems for hyperparameter learning/identification and experimental design, for instance, to find optimal regularisation parameters and forward operators. However, computationally, the…

We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along…

We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…

We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…

In this manuscript we propose and analyze an implicit two-point type method (or inertial method) for obtaining stable approximate solutions to linear ill-posed operator equations. The method is based on the iterated Tikhonov (iT) scheme. We…

Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…

Bilevel optimization has witnessed a resurgence of interest, driven by its critical role in trustworthy and efficient AI applications. While many recent works have established convergence to stationary points or local minima, obtaining the…

Bilevel optimization recently has attracted increased interest in machine learning due to its many applications such as hyper-parameter optimization and meta learning. Although many bilevel methods recently have been proposed, these methods…

In this paper, we study a consensus-based optimization method for nonconvex bi-level optimization, where the objective is to minimize an upper-level function over the set of global minimizers of a lower-level problem. The proposed approach…

We present some first results concerning a gradient-based dynamic approach to multi-objective optimization problems, involving inertial effects. We prove the existence of global solution trajectories for this second-order differential…

In this paper, we propose a proximal iteratively reweighted algorithm with extrapolation based on block coordinate update aimed at solving a class of optimization problems which is the sum of a smooth possibly nonconvex loss function and a…

Bilevel optimization is a key framework in hierarchical decision-making, where one problem is embedded within the constraints of another. In this work, we propose a control-theoretic approach to solving bilevel optimization problems. Our…