Related papers: Uniform non-convex optimisation via Extremum Seeki…
We investigate the fundamental optimization question of minimizing a target function $f$, whose gradients are expensive to compute or have limited availability, given access to some auxiliary side function $h$ whose gradients are cheap or…
Extremum seeking (ES) optimization approach has been very popular due to its non-model based analysis and implementation. This approach has been mostly used with gradient based search algorithms. Since least squares (LS) algorithms are…
We use proof mining techniques to obtain a uniform rate of asymptotic regularity for the instance of the parallel algorithm used by L\'opez-Acedo and Xu to find common fixed points of finite families of $k$-strict pseudocontractive…
For a map that is strictly but not strongly convex, model-based gradient extremum seeking has an eigenvalue of zero at the extremum, i.e., it fails at exponential convergence. Interestingly, perturbation-based model-free extremum seeking…
A unified approach to derive optimal finite differences is presented which combines three critical elements for numerical performance especially for multi-scale physical problems, namely, order of accuracy, spectral resolution and…
We consider a quasi-variational inequality governed by a moving set. We employ the assumption that the movement of the set has a small Lipschitz constant. Under this requirement, we show that the quasi-variational inequality has a unique…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
Our recently developed "unbiased" extremum seeking (uES) algorithms ensure perfect convergence to the optimum at a user-assigned exponential rate or, more powerfully, within a user-prescribed time. Unlike classical approach, these…
Many science and engineering applications feature non-convex optimization problems where the objective function can not be handled analytically, i.e. it is a black box. Examples include design optimization via experiments, or via costly…
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 discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…
The paper is devoted to a special Mirror Descent algorithm for problems of convex minimization with functional constraints. The objective function may not satisfy the Lipschitz condition, but it must necessarily have the Lipshitz-continuous…
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…
In this article, we present a greedy algorithm based on a tensor product decomposition, whose aim is to compute the global minimum of a strongly convex energy functional. We prove the convergence of our method provided that the gradient of…
This paper proposes a novel distributed optimization framework that addresses time-varying optimization problems without requiring explicit derivative information of the objective functions. Traditional distributed methods often rely on…
We consider first-order methods with constant step size for minimizing locally Lipschitz coercive functions that are tame in an o-minimal structure on the real field. We prove that if the method is approximated by subgradient trajectories,…
Shortened abstract: Given a constrained minimization problem, under what conditions does there exist a related, unconstrained problem having the same minimum points? This basic question in global optimization motivates this paper, which…
Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…
In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth…
We study the stability of entropically regularized optimal transport with respect to the marginals. Lipschitz continuity of the value and H\"older continuity of the optimal coupling in $p$-Wasserstein distance are obtained under general…