Related papers: Integer factorization and Riemann's hypothesis: Wh…
The problem of approximate joint diagonalization of a collection of matrices arises in a number of diverse engineering and signal processing problems. This problem is usually cast as an optimization problem, and it is the main goal of this…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
Polynomial factorization over $ZZ$ is of great historical and practical importance. Currently, the standard technique is to factor the polynomial over finite fields first and then to lift to integers. Factorization over finite fields can be…
We investigate the problem of factorization of large numbers on a quantum computer which we imagine to be realized within a linear ion trap. We derive upper bounds on the size of the numbers that can be factorized on such a quantum…
Mathematical optimization, although often leading to NP-hard models, is now capable of solving even large-scale instances within reasonable time. However, the primary focus is often placed solely on optimality. This implies that while…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…
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…
We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes…
Combinatorial optimization problems are considered to be an application, where quantum computing can have transformative impact. In the industrial context, job shop scheduling problems that aim at finding the optimal schedule for a set of…
We study a class of robust assortment optimization problems that was proposed by Farias, Jagabathula, and Shah (2013). The goal in these problems is to find an assortment that maximizes a firm's worst-case expected revenue under all…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
The difficulty of factoring large integers into primes is the basis for cryptosystems such as RSA. Due to the widespread popularity of RSA, there have been many proposed attacks on the factorization problem such as side-channel attacks…
In this paper, we create a systematic and automatic procedure for transforming the integer factorization problem into the problem of solving a system of Boolean equations. Surprisingly, the resulting system of Boolean equations takes on a…
We examine the problem of allocating a given total storage budget in a distributed storage system for maximum reliability. A source has a single data object that is to be coded and stored over a set of storage nodes; it is allowed to store…
The bound to factor large integers is dominated by the computational effort to discover numbers that are smooth, typically performed by sieving a polynomial sequence. On a von Neumann architecture, sieving has log-log amortized time…
Two-phase methods are commonly used to solve bi-objective combinatorial optimization problems. In the first phase, all extreme supported nondominated points are generated through a dichotomic search. This phase also allows the…
Efficient embedding virtual clusters in physical network is a challenging problem. In this paper we consider a scenario where physical network has a structure of a balanced tree. This assumption is justified by many real- world…
This thesis investigates the use of problem-specific knowledge to enhance a genetic algorithm approach to multiple-choice optimisation problems.It shows that such information can significantly enhance performance, but that the choice of…
We propose a localized divide and conquer algorithm for inverse factorization $S^{-1} = ZZ^*$ of Hermitian positive definite matrices $S$ with localized structure, e.g. exponential decay with respect to some given distance function on the…