Related papers: Derivative-Free Multiobjective Trust Region Descen…
Predictive estimation, which comprises model calibration, model prediction, and validation, is a common objective when performing inverse uncertainty quantification (UQ) in diverse scientific applications. These techniques typically require…
Optimization problems with nonlinear cost functions and combinatorial constraints appear in many real-world applications but remain challenging to solve efficiently compared to their linear counterparts. To bridge this gap, we propose…
Efficient optimization remains a fundamental challenge across numerous scientific and engineering domains, especially when objective function and gradient evaluations are computationally expensive. While zeroth-order optimization methods…
In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a…
A radial basis function (RBF) based sequential surrogate reliability method (SSRM) is proposed, in which a special optimization problem is solved to update the surrogate model of the limit state function (LSF) iteratively. The objective of…
Decision support systems often rely on solving complex optimization problems that may require to estimate uncertain parameters beforehand. Recent studies have shown how using traditionally trained estimators for this task can lead to…
In this work, the author presents a novel method for finding descent directions shared by two or more differentiable functions defined on the same unconstrained domain space. Then, the author illustrates an alternative Multiple-Gradient…
One method to solve expensive black-box optimization problems is to use a surrogate model that approximates the objective based on previous observed evaluations. The surrogate, which is cheaper to evaluate, is optimized instead to find an…
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…
In multi-objective design tasks, the computational cost increases rapidly when high-fidelity simulations are used to evaluate objective functions. Surrogate models help mitigate this cost by approximating the simulation output, simplifying…
We explore a hybrid technique to quantify the variability in the numerical solutions to a free boundary problem associated with magnetic equilibrium in axisymmetric fusion reactors amidst parameter uncertainties. The method aims at reducing…
In this article, we extend our previous work (Applicable Analysis, 2024, pp. 1-25) on the steepest descent method for uncertain multiobjective optimization problems. While that study established local convergence, it did not address global…
This work proposes a framework for large-scale stochastic derivative-free optimization (DFO) by introducing STARS, a trust-region method based on iterative minimization in random subspaces. This framework is both an algorithmic and…
The offline time of the reduced basis method can be very long given a large training set of parameter samples. This usually happens when the system has more than two independent parameters. On the other hand, if the training set includes…
Stochastic inverse problems are generally solved by some form of finite sampling of a space of uncertain parameters. For computationally expensive models, surrogate response surfaces are often employed to increase the number of samples used…
This paper presents a methodological framework for training, self-optimising, and self-organising surrogate models to approximate and speed up multiobjective optimisation of technical systems based on multiphysics simulations. At the hand…
We present DFO-GN, a derivative-free version of the Gauss-Newton method for solving nonlinear least-squares problems. As is common in derivative-free optimization, DFO-GN uses interpolation of function values to build a model of the…
Deep learning has proven to be effective in a wide variety of loss minimization problems. However, many applications of interest, like minimizing projected Bellman error and min-max optimization, cannot be modelled as minimizing a scalar…
We consider a class of stochastic programming problems where the implicitly decision-dependent random variable follows a nonparametric regression model with heteroscedastic error. The Clarke subdifferential and surrogate functions are not…
Surrogate models provide a low computational cost alternative to evaluating expensive functions. The construction of accurate surrogate models with large numbers of independent variables is currently prohibitive because it requires a large…