Related papers: Solving an inverse elliptic coefficient problem by…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
This paper addresses the estimation of uncertain distributed diffusion coefficients in elliptic systems based on noisy measurements of the model output. We formulate the parameter identification problem as an infinite dimensional…
In this paper, we study randomized and cyclic coordinate descent for convex unconstrained optimization problems. We improve the known convergence rates in some cases by using the numerical semidefinite programming performance estimation…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
We study the Levenberg-Marquardt (L-M) method for solving the highly nonlinear and ill-posed inverse problem of identifying the Robin coefficients in elliptic and parabolic systems. The L-M method transforms the Tikhonov regularized…
These lecture notes summarize various summer schools that I have given on the topic of solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a…
The paper covers a formulation of the inverse quadratic programming problem in terms of unconstrained optimization where it is required to find the unknown parameters (the matrix of the quadratic form and the vector of the quasi-linear part…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…
We examine robust output feedback control of discrete-time nonlinear systems with bounded uncertainties affecting the dynamics and measurements. Specifically, we demonstrate how to construct semi-infinite programs that produce gains to…
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
In this work, we show the consistency of an approach for solving robust optimization problems using sequences of sub-problems generated by ergodic measure preserving transformations. The main result of this paper is that the minimizers and…
Hybrid inverse problems are based on the interplay of two types of waves, in order to allow for imaging with both high resolution and high contrast. The inversion procedure often consists of two steps: first, internal measurements involving…
We study the inverse problem of recovering the order and the diffusion coefficient of an elliptic fractional partial differential equation from a finite number of noisy observations of the solution. We work in a Bayesian framework and show…
Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…
This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…
The implementation of computational sensing strategies often faces calibration problems typically solved by means of multiple, accurately chosen training signals, an approach that can be resource-consuming and cumbersome. Conversely, blind…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…