相关论文: Lipschitz gradients for global optimization in a o…
In the paper, the global optimization problem of a multidimensional "black-box" function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. A new efficient algorithm for solving this…
In many practical decision-making problems it happens that functions involved in optimization process are black-box with unknown analytical representations and hard to evaluate. In this paper, a global optimization problem is considered…
This paper deals with two kinds of the one-dimensional global optimization problems over a closed finite interval: (i) the objective function $f(x)$ satisfies the Lipschitz condition with a constant $L$; (ii) the first derivative of $f(x)$…
In this paper, the global optimization problem $\min_{y\in S} F(y)$ with $S$ being a hyperinterval in $\Re^N$ and $F(y)$ satisfying the Lipschitz condition with an unknown Lipschitz constant is considered. It is supposed that the function…
In this paper, global optimization (GO) Lipschitz problems are considered where the multi-dimensional multiextremal objective function is determined over a hyperinterval. An efficient one-dimensional GO method using local tuning on the…
Lipschitz one-dimensional constrained global optimization (GO) problems where both the objective function and constraints can be multiextremal and non-differentiable are considered in this paper. Problems, where the constraints are verified…
Global minimization is a fundamental challenge in optimization, especially in machine learning, where finding the global minimum of a function directly impacts model performance and convergence. This article introduces a novel optimization…
We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…
This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…
We introduce in this paper an optimal first-order method that allows an easy and cheap evaluation of the local Lipschitz constant of the objective's gradient. This constant must ideally be chosen at every iteration as small as possible,…
Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust…
This paper addresses the study of derivative-free smooth optimization problems, where the gradient information on the objective function is unavailable. Two novel general derivative-free methods are proposed and developed for minimizing…
The Lipschitz constant is an important quantity that arises in analysing the convergence of gradient-based optimization methods. It is generally unclear how to estimate the Lipschitz constant of a complex model. Thus, this paper studies an…
This article considers a box-constrained global optimization problem for Lipschitz-continuous functions with an unknown Lipschitz constant. Motivated by the famous DIRECT (DIviding RECTangles), a new HALRECT (HALving RECTangles) algorithm…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
A gradient-free deterministic method is developed to solve global optimization problems for Lipschitz continuous functions defined in arbitrary path-wise connected compact sets in Euclidean spaces. The method can be regarded as granular…
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…
In this paper, Lipschitz univariate constrained global optimization problems where both the objective function and constraints can be multiextremal are considered. The constrained problem is reduced to a discontinuous unconstrained problem…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
The goal of the paper is to design sequential strategies which lead to efficient optimization of an unknown function under the only assumption that it has a finite Lipschitz constant. We first identify sufficient conditions for the…