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This paper presents a comprehensive review of techniques proposed in the literature for solving bilevel optimization problems encountered in various real-life applications. Bilevel optimization is an appropriate choice for hierarchical…
With the widespread use of shared-nothing clusters of servers, there has been a proliferation of distributed object stores that offer high availability, reliability and enhanced performance for MapReduce-style workloads. However, relational…
We address the problem of unsupervised domain adaptation under the setting of generalized target shift (joint class-conditional and label shifts). For this framework, we theoretically show that, for good generalization, it is necessary to…
In this paper, we introduce and analyze a new low-rank multilevel strategy for the solution of random diffusion problems. Using a standard stochastic collocation scheme, we first approximate the infinite dimensional random problem by a…
Performance and reliability of content access in mobile networks is conditioned by the number and location of content replicas deployed at the network nodes. Facility location theory has been the traditional, centralized approach to study…
This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically…
This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…
The dynamic formulation of optimal transport has attracted growing interests in scientific computing and machine learning, and its computation requires to solve a PDE-constrained optimization problem. The classical Eulerian discretization…
Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in…
Linear programming has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of…
This paper presents the design and analysis of parallel approximation algorithms for facility-location problems, including $\NC$ and $\RNC$ algorithms for (metric) facility location, $k$-center, $k$-median, and $k$-means. These problems…
Placement is crucial in the physical design, as it greatly affects power, performance, and area metrics. Recent advancements in analytical methods, such as DREAMPlace, have demonstrated impressive performance in global placement. However,…
Localization in a pre-built map is a basic technique for robot autonomous navigation. Existing mapping and localization methods commonly work well in small-scale environments. As a map grows larger, however, more memory is required and…
We study the consequences of the equivalence between the least gradient problem and a boundary-to-boundary optimal transport problem in two dimensions. We extend the relationship between the two problems to their respective dual problems,…
Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution…
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
The basic optimal transportation problem consists in finding the most effective way of moving masses from one location to another, while minimizing the transportation cost. Such concept has been found to be useful to understand various…
In this paper we consider a distributed optimization scenario in which a set of processors aims at minimizing the maximum of a collection of "separable convex functions" subject to local constraints. This set-up is motivated by peak-demand…
In this paper, we study a spline collocation method for a numerical solution to the optimal transport problem We mainly solve the \MAE with the second boundary condition numerically by proposing a center matching algorithm. We prove a…
We consider the localization problem of multiple wideband sources in a multi-path environment by coherently taking into account the attenuation characteristics and the time delays in the reception of the signal. Our proposed method leaves…