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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…
We describe the optimization algorithm implemented in the open-source derivative-free solver RBFOpt. The algorithm is based on the radial basis function method of Gutmann and the metric stochastic response surface method of Regis and…
Efficient global optimization is the problem of minimizing an unknown function f, using as few evaluations f(x) as possible. It can be considered as a continuum-armed bandit problem, with noiseless data and simple regret. Expected…
Efficient Global Optimization (EGO) is widely used for the optimization of computationally expensive black-box functions. It uses a surrogate modeling technique based on Gaussian Processes (Kriging). However, due to the use of a stationary…
In many global optimization problems motivated by engineering applications, the number of function evaluations is severely limited by time or cost. To ensure that each evaluation contributes to the localization of good candidates for the…
Consider the problem of finding an optimal value of some objective functional subject to constraints over numerical domain. This type of problem arises frequently in practical engineering tasks. Nowdays almost all general methods for…
Gravitational field modelling is an important tool for inferring past and present dynamic processes of the Earth. Functions on the sphere such as the gravitational potential are usually expanded in terms of either spherical harmonics or…
Global optimisation to optimise expensive-to-evaluate black-box functions without gradient information. Bayesian optimisation, one of the most well-known techniques, typically employs Gaussian processes as surrogate models, leveraging their…
Optimization problems routinely depend on uncertain parameters that must be predicted before a decision is made. Classical robust and regret formulations are designed to handle erroneous predictions and can provide statistical error bounds…
Nonconvex optimization refers to the process of solving problems whose objective or constraints are nonconvex. Historically, this type of problems have been very difficult to solve to global optimality, with traditional solvers often…
A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many…
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…
We present an optimization algorithm that can identify a global minimum of a potentially nonconvex smooth function with high probability, assuming the Gibbs measure of the potential satisfies a logarithmic Sobolev inequality. Our…
The development and identification of effective optimization algorithms for non-convex real-world problems is a challenge in global optimization. Because theoretical performance analysis is difficult, and problems based on models of…
Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…
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…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
Localized collocation methods based on radial basis functions (RBFs) for elliptic problems appear to be non-robust in the presence of Neumann boundary conditions. In this paper we overcome this issue by formulating the RBF-generated finite…
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…