Related papers: An Efficient Interval Uncertainty Optimization App…
Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the…
In this paper, we propose a quasi Newton method to solve the robust counterpart of an uncertain multiobjective optimization problem under an arbitrary finite uncertainty set. Here the robust counterpart of an uncertain multiobjective…
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:…
In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…
This paper considers the linear-quadratic dual control problem where the system parameters need to be identified and the control objective needs to be optimized in the meantime. Contrary to existing works on data-driven linear-quadratic…
As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set,…
Data following an interval structure are increasingly prevalent in many scientific applications. In medicine, clinical events are often monitored between two clinical visits, making the exact time of the event unknown and generating…
We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated…
We consider the sparse optimization problem with nonlinear constraints and an objective function, which is given by the sum of a general smooth mapping and an additional term defined by the $ \ell_0 $-quasi-norm. This term is used to obtain…
In sparse optimization, enforcing hard constraints using the $\ell_0$ pseudo-norm offers advantages like controlled sparsity compared to convex relaxations. However, many real-world applications demand not only sparsity constraints but also…
Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…
We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined and the possible impact of…
Uncertainty quantification is essential for scientific analysis, as it allows for the evaluation and interpretation of variability and reliability in complex systems and datasets. In their original form, multivariate statistical regression…
Recently several methods were proposed for sparse optimization which make careful use of second-order information [10, 28, 16, 3] to improve local convergence rates. These methods construct a composite quadratic approximation using Hessian…
We study an optimization-based approach to construct statistically accurate confidence intervals for simulation performance measures under nonparametric input uncertainty. This approach computes confidence bounds from simulation runs driven…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving empirical risk minimization (ERM) problems with a nonsmooth regularization term. Our algorithm is applicable…
Quantification of the impact of uncertainty in material properties as well as the input ground motion on structural responses is an important step in implementing a performance-based earthquake engineering (PBEE) framework. Among various…
We consider the general nonlinear optimization problem where the objective function has an additional term defined by the $ \ell_0 $-quasi-norm in order to promote sparsity of a solution. This problem is highly difficult due to its…
We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic…
Uncertainty quantification for estimation through stochastic optimization solutions in an online setting has gained popularity recently. This paper introduces a novel inference method focused on constructing confidence intervals with…