Related papers: Large N Optimization for multi-matrix systems
We propose and analyze a set of variational quantum algorithms for solving quadratic unconstrained binary optimization problems where a problem consisting of $n_c$ classical variables can be implemented on $\mathcal O(\log n_c)$ number of…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when…
The space of invariants for a single matrix is generated by traces containing at most $N$ matrices per trace. We extend this analysis to multi-matrix models at finite $N$. Using the Molien-Weyl formula, we compute partition functions for…
We present a technique for optimizing hundreds of thousands of variational parameters in variational quantum Monte Carlo. By introducing iterative Krylov subspace solvers and by multiplying by the Hamiltonian and overlap matrices as they…
In this paper, we tackle the resolution of chance-constrained problems reformulated via Sample Average Approximation. The resulting data-driven deterministic reformulation takes the form of a large-scale mixed-integer program cursed with…
This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
Multi-cut critical points and their macroscopic loop amplitudes are studied in the multi-cut two-matrix models, based on an extension of the prescription developed by Daul, Kazakov and Kostov. After identifying possible critical points and…
Coded distributed computing has been considered as a promising technique which makes large-scale systems robust to the "straggler" workers. Yet, practical system models for distributed computing have not been available that reflect the…
Mathematical optimization is one of the cornerstones of modern engineering research and practice. Yet, throughout all application domains, mathematical optimization is, for the most part, considered to be a numerical discipline.…
We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity…
Nonnegative matrix factorization is the following problem: given a nonnegative input matrix $V$ and a factorization rank $K$, compute two nonnegative matrices, $W$ with $K$ columns and $H$ with $K$ rows, such that $WH$ approximates $V$ as…
A subspace method is introduced to solve large-scale trace ratio problems. This approach is matrix-free, requiring only the action of the two matrices involved in the trace ratio. At each iteration, a smaller trace ratio problem is…
We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise…
Higher order calculations in perturbative Quantum Field Theories often produce coupled linear systems of differential equations which factorize to first order. Here we present an algorithm to solve such systems in terms of iterated…
The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with $N$ samples behaves like $1/\sqrt{N}$. This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in…
In optimization routines used for on-line Model Predictive Control (MPC), linear systems of equations are usually solved in each iteration. This is true both for Active Set (AS) methods as well as for Interior Point (IP) methods, and for…
Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We…