Related papers: Global Optimization Algorithm through High-Resolut…

We study sampling problems associated with non-convex potentials that meanwhile lack smoothness. In particular, we consider target distributions that satisfy either logarithmic-Sobolev inequality or Poincar\'e inequality. Rather than…

There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…

We consider convex optimization with non-smooth objective function and log-concave sampling with non-smooth potential (negative log density). In particular, we study two specific settings where the convex objective/potential function is…

This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…

The paper considers a distributed algorithm for global minimization of a nonconvex function. The algorithm is a first-order consensus + innovations type algorithm that incorporates decaying additive Gaussian noise for annealing, converging…

Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The…

In the field of global optimization, many existing algorithms face challenges posed by non-convex target functions and high computational complexity or unavailability of gradient information. These limitations, exacerbated by sensitivity to…

We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…

We consider the global minimization of smooth functions based solely on function evaluations. Algorithms that achieve the optimal number of function evaluations for a given precision level typically rely on explicitly constructing an…

We introduce a derivative-free global optimization algorithm that efficiently computes minima for various classes of one-dimensional functions, including non-convex, and non-smooth functions.This algorithm numerically approximates the…

We study sampling problems associated with potentials that lack smoothness. The potentials can be either convex or non-convex. Departing from the standard smooth setting, the potentials are only assumed to be weakly smooth or non-smooth, or…

We propose a Langevin diffusion-based algorithm for non-convex optimization and sampling on a product manifold of spheres. Under a logarithmic Sobolev inequality, we establish a guarantee for finite iteration convergence to the Gibbs…

This paper studies first order methods for solving smooth minimax optimization problems $\min_x \max_y g(x,y)$ where $g(\cdot,\cdot)$ is smooth and $g(x,\cdot)$ is concave for each $x$. In terms of $g(\cdot,y)$, we consider two settings --…

This article presents a zeroth order probabilistic global optimization algorithm -- SwiftNav -- for (not necessarily convex) functions over a compact domain. A discretization procedure is deployed on the compact domain, starting with a…

In this paper, we provide new insights on the Unadjusted Langevin Algorithm. We show that this method can be formulated as a first order optimization algorithm of an objective functional defined on the Wasserstein space of order $2$. Using…

This paper proposes a universal algorithm for convex minimization problems of the composite form $g_0(x)+h(g_1(x),\dots, g_m(x)) + u(x)$. We allow each $g_j$ to independently range from being nonsmooth Lipschitz to smooth, from convex to…

This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…

We propose an algorithm to approximate solutions of global optimization problems in Sobolev spaces that follows the spirit of Consensus-based algorithms in finite dimensions. The main ingredient are Gaussian processes. In fact, we exploit…

This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…

An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…