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In probability theory and statistics notions of correlation among random variables, decay of correlation, and bias-variance trade-off are fundamental. In this work we introduce analogous notions in optimization, and we show their usefulness…
This article provides numerical evidence that under volume constraint the ball is the set which maximizes the perimeter of the least-perimeter partition into cells with prescribed areas. We introduce a numerical maximization algorithm which…
We study the wireless scheduling problem in the SINR model. More specifically, given a set of $n$ links, each a sender-receiver pair, we wish to partition (or \emph{schedule}) the links into the minimum number of slots, each satisfying…
We study 4d $\mathcal{N}=1$ supersymmetric theories on a compact Euclidean manifold of the form $S^1 \times\mathcal{M}_3$. Partition functions of gauge theories on this background can be computed using localization, and explicit formulas…
We present an algorithm to compute the geodesic $L_1$ farthest-point Voronoi diagram of $m$ point sites in the presence of $n$ rectangular obstacles in the plane. It takes $O(nm+n \log n + m\log m)$ construction time using $O(nm)$ space.…
We describe the topological cluster classification (TCC) algorithm. The TCC detects local structures with bond topologies similar to isolated clusters which minimise the potential energy for a number of monatomic and binary simple liquids…
The combinatorial optimization problem is one of the important applications in neural network computation. The solutions of linearly constrained continuous optimization problems are difficult with an exact algorithm, but the algorithm for…
The topological patterns exhibited by many real-world networks motivate the development of topology-based methods for assessing the similarity of networks. However, extracting topological structure is difficult, especially for large and…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…
The convergence performance of distributed optimization algorithms is of significant importance to solve optimal power flow (OPF) in a distributed fashion. In this paper, we aim to provide some insights on how to partition a power system to…
There is no question to the fact that electric vehicles (EVs) are the most viable solution to the climate change that the planet has long been combating. Along the same line, it is a salient subject to expand the availability of charging…
For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering…
We introduce new methods for the numerical solution of general Hamiltonian boundary value problems. The main feature of the new formulae is to produce numerical solutions along which the energy is precisely conserved, as is the case with…
In the present paper, the Polyak's principle, concerning convexity of the images of small balls through C1,1 mappings, is employed in the study of vector optimization problems. This leads to extend to such a context achievements of local…
We consider an energy minimization problem for cooperative LTE networks. To reduce energy consumption, we investigate how to jointly optimize the transmit power and the association between cells and user equipments (UEs), by taking into…
In this paper, we consider the problem of optimally coordinating the response of a group of distributed energy resources (DERs) so they collectively meet the electric power demanded by a collection of loads, while minimizing the total…
In this work, we mainly present the optimal convergence rates of the temporally second-order finite element scheme for solving the electrohydrodynamic equation. Suffering from the highly coupled nonlinearity, the convergence analysis of the…
In this paper, we study locating charging station problem as facility location problem and its variants ($k$-Median, $k$-Facility location and $k$-center). We study the connectivity and the capacity constraints in these problem. Capacity…
For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach…
Centrality measures, quantifying the importance of vertices or edges, play a fundamental role in network analysis. To date, triggered by some positive approximability results, a large body of work has been devoted to studying centrality…