Related papers: Lipschitz gradients for global optimization in a o…
The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…
The paper is devoted to new modifications of recently proposed adaptive methods of Mirror Descent for convex minimization problems in the case of several convex functional constraints. Methods for problems of two classes are considered. The…
In this paper we consider a distributed stochastic optimization problem without the gradient/subgradient information for the local objective functions, subject to local convex constraints. The objective functions may be non-smooth and…
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…
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, a new theory is developed for first-order stochastic convex optimization, showing that the global convergence rate is sufficiently quantified by a local growth rate of the objective function in a neighborhood of the optimal…
We study the problem of zeroth-order (black-box) optimization of a Lipschitz function $f$ defined on a compact subset $\mathcal X$ of $\mathbb R^d$, with the additional constraint that algorithms must certify the accuracy of their…
Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…
This paper propose a new frame work for finding global minima which we call optimization by cut. In each iteration, it takes some samples from the feasible region and evaluates the objective function at these points. Based on the…
We consider the optimization problem of the form $\min_{x \in \mathbb{R}^d} f(x) \triangleq \mathbb{E}_{\xi} [F(x; \xi)]$, where the component $F(x;\xi)$ is $L$-mean-squared Lipschitz but possibly nonconvex and nonsmooth. The recently…
Bayesian optimization and Lipschitz optimization have developed alternative techniques for optimizing black-box functions. They each exploit a different form of prior about the function. In this work, we explore strategies to combine these…
Black-box global optimization aims at minimizing an objective function whose analytical form is not known. To do so, many state-of-the-art methods rely on sampling-based strategies, where sampling distributions are built in an iterative…
The problem of minimization of the sum of two convex functions has various theoretical and real-world applications. One of the popular methods for solving this problem is the proximal gradient method (proximal forward-backward algorithm). A…
This paper considers optimization of smooth nonconvex functionals in smooth infinite dimensional spaces. A H\"older gradient descent algorithm is first proposed for finding approximate first-order points of regularized polynomial…
We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where…
The Lipschitz constant of a response surface function upper bounds the sensitivity of a dependent variable to changes in the independent ones. Traditionally, such constants have found much implicit and abstract use in mathematically…
Optimization problems arising in data science have given rise to a number of new derivative-based optimization methods. Such methods often use standard smoothness assumptions -- namely, global Lipschitz continuity of the gradient function…
We consider the computation of an approximately stationary point for a Lipschitz and semialgebraic function $f$ with a local oracle. If $f$ is smooth, simple deterministic methods have dimension-free finite oracle complexities. For the…
Distributed optimization utilizes local computation and communication to realize a global aim of optimizing the sum of local objective functions. This article addresses a class of constrained distributed nonconvex optimization problems…
This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed an optimized gradient method (OGM) for this problem and…