Related papers: Acceleration of univariate global optimization alg…
A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be…
The problem of minimizing the maximum of $N$ convex, Lipschitz functions plays significant roles in optimization and machine learning. It has a series of results, with the most recent one requiring $O(N\epsilon^{-2/3} + \epsilon^{-8/3})$…
This paper addresses the challenge of dynamic multi-objective optimization problems (DMOPs) by introducing novel approaches for accelerating prediction strategies within the evolutionary algorithm framework. Since the objectives of DMOPs…
In this article we investigate the possibilities of accelerating the double smoothing technique when solving unconstrained nondifferentiable convex optimization problems. This approach relies on the regularization in two steps of the…
We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective…
Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…
Recently, accelerated algorithms using the anchoring mechanism for minimax optimization and fixed-point problems have been proposed, and matching complexity lower bounds establish their optimality. In this work, we present the surprising…
In the development of first-order methods for smooth (resp., composite) convex optimization problems, where smooth functions with Lipschitz continuous gradients are minimized, the gradient (resp., gradient mapping) norm becomes a…
In this paper, we propose some accelerated methods for solving optimization problems under the condition of relatively smooth and relatively Lipschitz continuous functions with an inexact oracle. We consider the problem of minimizing the…
We consider a multi-agent framework for distributed optimization where each agent has access to a local smooth strongly convex function, and the collective goal is to achieve consensus on the parameters that minimize the sum of the agents'…
We further research on the accelerated optimization phenomenon on Riemannian manifolds by introducing accelerated global first-order methods for the optimization of $L$-smooth and geodesically convex (g-convex) or $\mu$-strongly g-convex…
We consider the minimization problem of a sum of a number of functions having Lipshitz $p$-th order derivatives with different Lipschitz constants. In this case, to accelerate optimization, we propose a general framework allowing to obtain…
This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending…
This work demonstrates the utility of gradients for the global optimization of certain differentiable functions with many suboptimal local minima. To this end, a principle for generating search directions from non-local quadratic…
We focus on nonconvex and nonsmooth minimization problems with a composite objective, where the differentiable part of the objective is freed from the usual and restrictive global Lipschitz gradient continuity assumption. This longstanding…
We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…
One of the actual problems in the field of numerical optimisation, as is well known, is the problem of the search for the global extremum of a multivariate function [1-9,13,14,17-21]. Various versions of the random search methods [6,8,9]…
Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have…
Arising in semi-parametric statistics, control applications, and as sub-problems in global optimization methods, certain optimization problems can have objective functions requiring numerical integration to evaluate, yet gradient function…
In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. However, existing first-order methods for solving such problems either are too…