Related papers: A trust-region framework for optimization using He…
Expensive multi-objective optimization problems (EMOPs) are common in real-world scenarios where evaluating objective functions is costly and involves extensive computations or physical experiments. Current Pareto set learning methods for…
This paper presents a novel learning-based approach to construct a surrogate problem that approximates a given parametric nonconvex optimization problem. The surrogate function is designed to be the minimum of a finite set of functions,…
We develop and analyze a method for stochastic simulation optimization based on Gaussian process models within a trust-region framework. We focus on settings where the variance of the objective function is large, making accurate estimation…
Solving optimization problems with unknown parameters often requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the…
Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer…
This study develops a hybrid ensemble-variational approach for solving data assimilation problems. The method, called TR-4D-EnKF, is based on a trust region framework and consists of three computational steps. First an ensemble of model…
In this paper, a meshless Hermite-HDMR finite difference method is proposed to solve high-dimensional Dirichlet problems. The approach is based on the local Hermite-HDMR expansion with an additional smoothing technique. First, we introduce…
We introduce a two-level trust-region method (TLTR) for solving unconstrained nonlinear optimization problems. Our method uses a composite iteration step, which is based on two distinct search directions. The first search direction is…
Derivative-Free Optimization (DFO) involves methods that rely solely on evaluations of the objective function. One of the earliest strategies for designing DFO methods is to adapt first-order methods by replacing gradients with…
We propose an optimization algorithm to improve the design and performance of quantum communication networks. When physical architectures become too complex for analytical methods, numerical simulation becomes essential to study quantum…
In this work we propose two Hermite-type optimization methods, Hermite least squares and Hermite BOBYQA, specialized for the case that some partial derivatives of the objective function are available and others are not. The main objective…
We develop an interior-point method for nonsmooth regularized bound-constrained optimization problems. Our method consists of iteratively solving a sequence of unconstrained nonsmooth barrier subproblems. We use a variant of the proximal…
Data assimilation presents computational challenges because many high-fidelity models must be simulated. Various deep-learning-based surrogate modeling techniques have been developed to reduce the simulation costs associated with these…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
Surrogate modeling is an essential data-driven technique for quantifying relationships between input variables and system responses in manufacturing and engineering systems. Two major challenges limit its effectiveness: (1) large data…
This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…
The difficulty of minimizing a nonconvex function is in part explained by the presence of saddle points. This slows down optimization algorithms and impacts worst-case complexity guarantees. However, many nonconvex problems of interest…
We propose a nonsmooth trust-region method for solving optimization problems with locally Lipschitz continuous functions, with application to problems constrained by variational inequalities of the second kind. Under suitable assumptions on…
Solving complex problems requires continuous effort in developing theory and practice to cope with larger, more difficult scenarios. Working with surrogates is normal for creating a proxy that realistically models the problem into the…
We propose a practical Bayesian optimization method over sets, to minimize a black-box function that takes a set as a single input. Because set inputs are permutation-invariant, traditional Gaussian process-based Bayesian optimization…