相关论文: Smoothing analysis of two robust multigrid methods…

Computational speed and global optimality are key needs for practical algorithms for the optimal power flow problem. Two convex relaxations offer a favorable trade-off between the standard second-order cone and the standard semidefinite…

In this paper, a new mixed integer nonlinear programming formulation is proposed for optimally placing and operating pressure reducing valves and chlorine booster stations in water distribution networks. The objective is the minimization of…

In this paper, we present new convex relaxations for nonconvex quadratically constrained quadratic programming (QCQP) problems. While recent research has focused on strengthening convex relaxations using reformulation-linearization…

We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…

We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…

Optimizing k-space sampling trajectories is a promising yet challenging topic for fast magnetic resonance imaging (MRI). This work proposes to optimize a reconstruction method and sampling trajectories jointly concerning image…

In this paper, we consider two distinct challenges in the resolution of nonsmooth stochastic optimization. Of these, the first pertains to the pronounced dependence of dimension in Gaussian smoothing-enabled zeroth-order schemes, impeding…

We study an iterative Galerkin method for quasilinear elliptic problems in the Browder-Minty setting. The resulting discrete nonlinear systems are solved by linearization via a (damped) Zarantonello iteration. Unlike prior work, adaptive…

We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the…

This work presents a general framework for solving the low rank and/or sparse matrix minimization problems, which may involve multiple non-smooth terms. The Iteratively Reweighted Least Squares (IRLS) method is a fast solver, which smooths…

We consider standard tracking-type, distributed elliptic optimal control problems with $L^2$ regularization, and their finite element discretization. We are investigating the $L^2$ error between the finite element approximation $u_{\varrho…

Quadratically constrained quadratic programs (QCQPs) are ubiquitous in optimization: Such problems arise in applications from operations research, power systems, signal processing, chemical engineering, and portfolio theory, among others.…

We introduce a new iterative rounding technique to round a point in a matroid polytope subject to further matroid constraints. This technique returns an independent set in one matroid with limited violations of the other ones. On top of the…

The octagonal shrinkage and clustering algorithm for regression (OSCAR), equipped with the $\ell_1$-norm and a pair-wise $\ell_{\infty}$-norm regularizer, is a useful tool for feature selection and grouping in high-dimensional data…

We shed new light on the \textit{smoothness} of optimization problems arising in prediction error parameter estimation of linear and nonlinear systems. We show that for regions of the parameter space where the model is not contractive, the…

Multi-robot systems offer enhanced capability over their monolithic counterparts, but they come at a cost of increased complexity in coordination. To reduce complexity and to make the problem tractable, multi-robot motion planning (MRMP)…

In this paper, we study linearly constrained policy optimization over the manifold of Schur stabilizing controllers, equipped with a Riemannian metric that emerges naturally in the context of optimal control problems. We provide extrinsic…

Many solid mechanics problems on complex geometries are conventionally solved using discrete boundary methods. However, such an approach can be cumbersome for problems involving evolving domain boundaries due to the need to track boundaries…

The Eilers-Whittaker method for data smoothing effectiveness depends on the choice of the regularisation parameter, and automatic selection is a necessity for large datasets. Common methods, such as leave-one-out cross-validation, can…

We aim to compute lifted stationary points of a sparse optimization problem (P0) with complementarity constraints. We define a continuous relaxation problem (Rv) that has the same global minimizers and optimal value with problem (P0).…