Related papers: On Cayley algorithm for double partition
We give short elementary expositions of combinatorial proofs of some variants of Euler's partitition problem that were first addressed analytically by George Andrews, and later combinatorially by others. Our methods, based on ideas from a…
We present a method to solve two-stage stochastic problems with fixed recourse when the uncertainty space can have either discrete or continuous distributions. Given a partition of the uncertainty space, the method is addressed to solve a…
In this paper, we present an exact algorithm for optimizing two linear fractional over the efficient set of a multi-objective integer quadratic problem. This type of problems arises when two decision-makers, such as firms, each have a…
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
We consider an inverse problem of determining coefficient matrices in an $N$-system of second-order elliptic equations in a bounded two dimensional domain by a set of Cauchy data on arbitrary subboundary. The main result of the article is…
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…
Seriation is a problem consisting of seeking the best enumeration order of a set of units whose interrelationship is described by a bipartite graph, that is, a graph whose nodes are partitioned in two sets and arcs only connect nodes in…
The problem of factorising positive integer $N$ into two integer factors $x$ and $y$ is first reformulated as an optimisation problem over the positive integer domain of either of the Diophantine polynomials $Q_N(x,y)=N^2(N-xy)^2 +…
An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…
The present work includes some of the author's original researches on integer solutions of Diophantine liner equations and systems. The notion of "general integer solution" of a Diophantine linear equation with two unknowns is extended to…
In this paper, we present efficient algorithms for solving the Diophantine equation $f(x, y) = m$ for an arbitrary definite binary quadratic form $f$, given the factorization of $m$. While Cornacchia's algorithm to solve $x^2 + dy^2 = m$ is…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
Given a set of integers W, the Partition problem determines whether W can be divided into two disjoint subsets with equal sums. We model the Partition problem as a system of polynomial equations, and then investigate the complexity of a…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
This paper presents an improved forward-backward splitting algorithm with two inertial parameters. It aims to find a point in the real Hilbert space at which the sum of a co-coercive operator and a maximal monotone operator vanishes. Under…
A novel canonical duality theory (CDT) is presented for solving general bilevel mixed integer nonlinear optimization governed by linear and quadratic knapsack problems. It shows that the challenging knapsack problems can be solved…
In this work a rationalized algorithm for calculating the quotient of two complex numbers is presented which reduces the number of underlying real multiplications. The performing of a complex number division using the naive method takes 4…
An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained…
How to handle division in systems that compute with logical formulas involving what would otherwise be polynomial constraints over the real numbers is a surprisingly difficult question. This paper argues that existing approaches from both…
In polynomial optimization problems, nonnegativity constraints are typically handled using the sum of squares condition. This can be efficiently enforced using semidefinite programming formulations, or as more recently proposed by Papp and…