Related papers: A robust alternating direction numerical scheme in…
In this paper, we propose a faster stochastic alternating direction method of multipliers (ADMM) for nonconvex optimization by using a new stochastic path-integrated differential estimator (SPIDER), called as SPIDER-ADMM. Moreover, we prove…
We propose the combination of forward shape derivatives and the use of an iterative inversion scheme for Bayesian optimization to find optimal designs of nanophotonic devices. This approach widens the range of applicability of Bayesian…
In this paper we propose an Alternating Direction Method of Multipliers (ADMM) algorithm for solving a Model Predictive Control (MPC) optimization problem, in which the system has state and input constraints and a nonlinear input map. The…
This paper is devoted to the analysis of a second order method for recovering the \emph{a priori} unknown shape of an inclusion $\omega$ inside a body $\Omega$ from boundary measurement. This inverse problem - known as electrical impedance…
Inverse problems in imaging are typically ill-posed and are usually solved by employing regularized optimization techniques. The usage of appropriate constraints can restrict the solution space, thus making it feasible for a reconstruction…
We propose to constrain segmentation functionals with a dimensionless, unbiased and position-independent shape compactness prior, which we solve efficiently with an alternating direction method of multipliers (ADMM). Involving a squared sum…
This work deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…
Inverse obstacle scattering is the recovery of an obstacle boundary from the scattering data produced by incident waves. This shape recovery can be done by iteratively solving a PDE-constrained optimization problem for the obstacle…
Sparse signal recovery based on nonconvex and nonsmooth optimization problems has significant applications and demonstrates superior performance in signal processing and machine learning. This work deals with a scale-invariant…
Since shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations, we show how shape optimization techniques can also be applied to an interface identification problem…
In many statistical modeling problems, such as classification and regression, it is common to encounter sparse and blocky coefficients. Sparse fused Lasso is specifically designed to recover these sparse and blocky structured features,…
We propose AD3, a new algorithm for approximate maximum a posteriori (MAP) inference on factor graphs based on the alternating directions method of multipliers. Like dual decomposition algorithms, AD3 uses worker nodes to iteratively solve…
This paper introduces a methodology designed to augment the inverse design optimization process in scenarios constrained by limited compute, through the strategic synergy of multi-fidelity evaluations, machine learning models, and…
In this paper, we propose a trajectory optimization for computing smooth collision free trajectories for nonholonomic curvature bounded vehicles among static and dynamic obstacles. One of the key novelties of our formulation is a hierarchal…
We propose two numerical algorithms in the fully nonconvex setting for the minimization of the sum of a smooth function and the composition of a nonsmooth function with a linear operator. The iterative schemes are formulated in the spirit…
This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…
We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are…
In image processing, Total Variation (TV) regularization models are commonly used to recover blurred images. One of the most efficient and popular methods to solve the convex TV problem is the Alternating Direction Method of Multipliers…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
Herein, we study an inverse problem for detecting unknown obstacles by the enclosure method using the Dirichlet--to--Neumann map for measurements. We justify the method for an penetrable obstacle case involving a biharmonic equation. We use…