Related papers: Semi-Definite Programming Relaxation for Non-Line-…
We proposed a new criterion \textit{noise-stability}, which revised the classical rigidity theory, for evaluation of MDS algorithms which can truthfully represent the fidelity of global structure reconstruction; then we proved the…
A hierarchy of semidefinite programming (SDP) relaxations approximates the global optimum of polynomial optimization problems of noncommuting variables. Generating the relaxation, however, is a computationally demanding task, and only…
As a model problem for clustering, we consider the densest k-disjoint-clique problem of partitioning a weighted complete graph into k disjoint subgraphs such that the sum of the densities of these subgraphs is maximized. We establish that…
Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…
In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted…
Distributed cooperative localization in wireless networks is a challenging problem since it typically requires solving a large-scale nonconvex and nonsmooth optimization problem. In this paper, we reformulate the classic cooperative…
The sensor network localization, SNL, problem in embedding dimension r, consists of locating the positions of wireless sensors, given only the distances between sensors that are within radio range and the positions of a subset of the…
Real-world network applications must cope with failing nodes, malicious attacks, or, somehow, nodes facing corrupted data --- classified as outliers. One enabling application is the geographic localization of the network nodes. However,…
Robustly and accurately localizing objects in real-world environments can be challenging due to noisy data, hardware limitations, and the inherent randomness of physical systems. To account for these factors, existing works estimate the…
In this paper, we give a new penalized semidefinite programming approach for non-convex quadratically-constrained quadratic programs (QCQPs). We incorporate penalty terms into the objective of convex relaxations in order to retrieve…
We consider robust discrete minimization problems where uncertainty is defined by a convex set in the objective. We show how an integrality gap verifier for the linear programming relaxation of the non-robust version of the problem can be…
This paper presents a method to estimate the 3D object position and occupancy given a set of object detections in multiple images and calibrated cameras. This problem is modelled as the estimation of a set of quadrics given 2D conics fit to…
We introduce a method for proving lower bounds on the efficacy of semidefinite programming (SDP) relaxations for combinatorial problems. In particular, we show that the cut, TSP, and stable set polytopes on $n$-vertex graphs are not the…
Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that…
For many practical problems and applications, it is not feasible to create a vast and accurately labeled dataset, which restricts the application of deep learning in many areas. Semi-supervised learning algorithms intend to improve…
We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and…
We propose a linear time and constant space algorithm for computing Euclidean projections onto sets on which a normalized sparseness measure attains a constant value. These non-convex target sets can be characterized as intersections of a…
We introduce a relaxation for homomorphism problems that combines semidefinite programming with linear Diophantine equations, and propose a framework for the analysis of its power based on the spectral theory of association schemes. We use…
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…
Quantifying the robustness of neural networks or verifying their safety properties against input uncertainties or adversarial attacks have become an important research area in learning-enabled systems. Most results concentrate around the…