Related papers: Global optimization in inverse problems: A compari…
Mixed membership factorization is a popular approach for analyzing data sets that have within-sample heterogeneity. In recent years, several algorithms have been developed for mixed membership matrix factorization, but they only guarantee…
This paper presents a novel algorithm integrating global and robust optimization methods to solve continuous non-convex quadratic problems under convex uncertainty sets. The proposed Robust spatial branch-and-bound (RsBB) algorithm combines…
The growing availability of computational resources has significantly increased the interest of the scientific community in performing complex multi-physics and multi-domain simulations. However, the generation of appropriate computational…
PDE-constrained optimization problems have been barely solved by radial basis functions (RBFs) methods [Pearson, 2013]. It is well known that RBF methods can attain an exponential rate of convergence when $C^{\infty}$ kernels are used,…
Inverse optimization (Inverse optimal control) is the task of imputing a cost function such that given test points (trajectories) are (nearly) optimal with respect to the discovered cost. Prior methods in inverse optimization assume that…
We consider the problem of global optimization with noisy zeroth order oracles - a well-motivated problem useful for various applications ranging from hyper-parameter tuning for deep learning to new material design. Existing work relies on…
In spatial statistics, a common method for prediction over a Gaussian random field (GRF) is maximum likelihood estimation combined with kriging. For massive data sets, kriging is computationally intensive, both in terms of CPU time and…
Global optimization of black-box functions from noisy samples is a fundamental challenge in machine learning and scientific computing. Traditional methods such as Bayesian Optimization often converge to local minima on multi-modal…
We consider the problem of maximizing an unknown function over a compact and convex set using as few observations as possible. We observe that the optimization of the function essentially relies on learning the induced bipartite ranking…
Recently, the regularized functional matching pursuit (RFMP) was introduced as a greedy algorithm for linear ill-posed inverse problems. This algorithm incorporates the Tikhonov-Phillips regularization which implies the necessity of a…
This paper proposes a new robust optimization (RO) formulation namely the RO under objective functional uncertainty (ObRO). The ObRO adopts a min-max structure where the inner problem finds the worst-case objective function in a continuous…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
This note carries three purposes involving our latest advances on the radial basis function (RBF) approach. First, we will introduce a new scheme employing the boundary knot method (BKM) to nonlinear convection-diffusion problem. It is…
We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global…
We address the problem of Gaussian Process (GP) optimization in the presence of unknown and potentially varying adversarial perturbations. Unlike traditional robust optimization approaches that focus on maximizing performance under…
Semi-lagrangian schemes for discretization of the dynamic programming principle are based on a time discretization projected on a state-space grid. The use of a structured grid makes this approach not feasible for high-dimensional problems…
Efficient global optimization is a widely used method for optimizing expensive black-box functions such as tuning hyperparameter, and designing new material, etc. Despite its popularity, less attention has been paid to analyzing the…
We propose and test the first Reduced Radial Basis Function Method (R$^2$BFM) for solving parametric partial differential equations on irregular domains. The two major ingredients are a stable Radial Basis Function (RBF) solver that has an…
A framework for robust optimization under uncertainty based on the use of the generalized inverse distribution function (GIDF), also called quantile function, is here proposed. Compared to more classical approaches that rely on the usage of…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…