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Data clustering is an instrumental tool in the area of energy resource management. One problem with conventional clustering is that it does not take the final use of the clustered data into account, which may lead to a very suboptimal use…
Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time…
Nonlinear energy functionals appearing in the calculus of variations can be discretized by the finite element (FE) method and formulated as a sum of energy contributions from local elements. A fast evaluation of energy functionals…
Bilevel programs with spatial price equilibrium constraints are strategic models that consider a price competition at the lower level. These models find application in facility location-price models, optimal bidding in power networks, and…
Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…
In this article we want to demonstrate the effectiveness of the new D-Wave quantum annealer, D-Wave 2000Q, in dealing with real world problems. In particular, it is shown how the quantum annealing process is able to find global optima even…
This paper proposes a distributed algorithm for a network of agents to solve an optimization problem with separable objective function and locally coupled constraints. Our strategy is based on reformulating the original constrained problem…
LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly efficient but remain…
We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…
Intermittent renewable energy resources like wind and solar pose great uncertainty of multiple time scales, from minutes to years, on the design and operation of power systems. Energy system optimization models have been developed to find…
Free energy landscapes encode the kinetics, intermediates, and transition states that govern molecular processes and are thus a key target of single biomolecule research. Typical approaches to deriving optimal, error-minimizing,…
Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to…
We propose a novel methodology for forecasting spatio-temporal data using supervised semi-nonnegative matrix factorization (SSNMF) with frequency regularization. Matrix factorization is employed to decompose spatio-temporal data into…
We propose a variant of the Simulated Annealing method for optimization in the multivariate analysis of differentiable functions. The method uses global actualizations via the Hybrid Monte Carlo algorithm in their generalized version for…
Vanishing gradients can pose substantial obstacles for high-dimensional optimization problems. Here we consider energy minimization problems for quantum many-body systems with extensive Hamiltonians and finite-range interactions, which can…
In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…
In this paper, we introduce a novel first-order dual gradient algorithm for solving network utility maximization problems that arise in resource allocation schemes over networks with safety-critical constraints. Inspired by applications…
The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…
We present a class of simple algorithms that allows to find the reaction path in systems with a complex potential energy landscape. The approach does not need any knowledge on the product state and does not require the calculation of any…