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We consider the problem of maximizing submodular functions; while this problem is known to be NP-hard, several numerically efficient local search techniques with approximation guarantees are available. In this paper, we propose a novel…
A method for model reduction in nonlinear ODE systems is demonstrated through computational examples. The method does not require an implicit separation of time-scales in the fine dynamics to be effective. From the computational standpoint,…
Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics - e.g., or the expected length of a shortest path between two…
A dynamic graph algorithm is a data structure that supports edge insertions, deletions, and specific problem queries. While extensive research exists on dynamic algorithms for graph problems solvable in polynomial time, most of these…
We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…
In solving mathematical optimization problems efficiently, it is crucial to make use of information about specific types of constraints, such as the one-hot or Special-Ordered Set (SOS) constraints. In many cases, exploiting such…
Deep learning models have achieved significant success in various image related tasks. However, they often encounter challenges related to computational complexity and overfitting. In this paper, we propose an efficient approach that…
Robust discrete optimization is a highly active field of research where a plenitude of combinations between decision criteria, uncertainty sets and underlying nominal problems are considered. Usually, a robust problem becomes harder to…
In this paper, we investigate the decentralized statistical inference problem, where a network of agents cooperatively recover a (structured) vector from private noisy samples without centralized coordination. Existing optimization-based…
Electric machine design optimization is a computationally expensive multi-objective optimization problem. While the objectives require time-consuming finite element analysis, optimization constraints can often be based on mathematical…
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…
Critical points of energy functionals, which are of broad interest, for instance, in physics and chemistry, in solid and quantum mechanics, in material science, or in general diffusion-reaction models arise as solutions to the associated…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
Despite advances in generative methods, accurately modeling the distribution of graphs remains a challenging task primarily because of the absence of predefined or inherent unique graph representation. Two main strategies have emerged to…
Benders decomposition is a widely used method for solving large optimization problems, but its performance is often hindered by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating…
This paper presents a theory of optimization fabrics, second-order differential equations that encode nominal behaviors on a space and can be used to define the behavior of a smooth optimizer. Optimization fabrics can encode commonalities…
The paper describes a general glance to the use of element exchange techniques for optimization over permutations. A multi-level description of problems is proposed which is a fundamental to understand nature and complexity of optimization…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
We address Stackelberg models of combinatorial congestion games (CCGs); we aim to optimize the parameters of CCGs so that the selfish behavior of non-atomic players attains desirable equilibria. This model is essential for designing such…
We study the problem of finding unitary submatrices of the $N \times N$ discrete Fourier transform matrix, in the context of interpolating a discrete bandlimited signal using an orthogonal basis. This problem is related to a diverse set of…