Related papers: Globally aware optimization with resurgence
A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information such as analytic continuability, position of singularities,…
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…
We study the convergence of a variant of distributed gradient descent (DGD) on a distributed low-rank matrix approximation problem wherein some optimization variables are used for consensus (as in classical DGD) and some optimization…
Contemporary global optimization algorithms are based on local measures of utility, rather than a probability measure over location and value of the optimum. They thus attempt to collect low function values, not to learn about the optimum.…
The advancement of artificial intelligence has cast a new light on the development of optimization algorithm. This paper proposes to learn a two-phase (including a minimization phase and an escaping phase) global optimization algorithm for…
We propose a new gradient descent algorithm with added stochastic terms for finding the global optimizers of nonconvex optimization problems. A key component in the algorithm is the adaptive tuning of the randomness based on the value of…
Our main aim in this self-contained article is at the same time to detail the relationships between the resurgence and the hyperasymptotic theories, and to demonstrate how these theories can be used for an implicit resurgent function. For…
Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to…
We propose a new globalization strategy that can be used in unconstrained optimization algorithms to support rapid convergence from remote starting points. Our approach is based on using multiple points at each iteration to build a…
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…
A new technique of global optimization and its applications in particular to neural networks are presented. The algorithm is also compared to other global optimization algorithms such as Gradient descent (GD), Monte Carlo (MC), Genetic…
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…
It is well known that perturbative expansions of path integrals are divergent. These expansions are to be understood as asymptotic expansions, which encode the limiting behaviour of the path integral for positive small coupling.…
This paper considers global optimization with a black-box unknown objective function that can be non-convex and non-differentiable. Such a difficult optimization problem arises in many real-world applications, such as parameter tuning in…
Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…
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…
Metasurfaces are subwavelength-structured artificial media that can shape and localize electromagnetic waves in unique ways. The inverse design of these devices is a non-convex optimization problem in a high dimensional space, making global…
Solving inverse problems in physics is central to understanding complex systems and advancing technologies in various fields. Iterative optimization algorithms, commonly used to solve these problems, often encounter local minima, chaos, or…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
This work addresses distributed optimization, where a network of agents wants to minimize a global strongly convex objective function. The global function can be written as a sum of local convex functions, each of which is associated with…