Related papers: Parallelization of Modular Algorithms
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…
We propose a sequential homotopy method for the solution of mathematical programming problems formulated in abstract Hilbert spaces under the Guignard constraint qualification. The method is equivalent to performing projected backward Euler…
We study existence and computability of finite bases for ideals of polynomials over infinitely many variables. In our setting, variables come from a countable logical structure A, and embeddings from A to A act on polynomials by renaming…
To integer programming problems, computational algebraic approaches using Grobner bases or standard pairs via the discreteness of toric ideals have been studied in recent years. Although these approaches have not given improved time…
In this paper, we examine the structure of systems that are weighted homogeneous for several systems of weights, and how it impacts the computation of Gr\"obner bases. We present several linear algebra algorithms for computing Gr\"obner…
We consider structured optimisation problems defined in terms of the sum of a smooth and convex function, and a proper, l.s.c., convex (typically non-smooth) one in reflexive variable exponent Lebesgue spaces $L_{p(\cdot)}(\Omega)$. Due to…
Recent strides in nonlinear model predictive control (NMPC) underscore a dependence on numerical advancements to efficiently and accurately solve large-scale problems. Given the substantial number of variables characterizing typical…
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…
To obtain a better understanding of the trade-offs between various objectives, Bi-Objective Integer Programming (BOIP) algorithms calculate the set of all non-dominated vectors and present these as the solution to a BOIP problem.…
In this paper, we present a modular strategy which describes key properties of the absolute primary decomposition of an equidimensional polynomial ideal defined by polynomials with rational coefficients. The algorithm we design is based on…
The problem of solving a system of polynomial equations is one of the most fundamental problems in applied mathematics. Among them, the problem of solving a system of binomial equations form a important subclass for which specialized…
We present a general approach to a modular frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert…
An algorithm is discussed for converting a class of recursive processes to a parallel system. It is argued that this algorithm can be superior to certain methods currently found in the literature for an important subset of problems. The…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
In this article we present an algorithm that uses the graded algebra structure of Hilbert modular forms to compute the adelic $q$-expansion of Hilbert modular forms of weight one as the quotient of Hilbert modular forms of higher weight.…
We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…
The theory of one-sided $M$-ideals and multipliers of operator spaces is simultaneously a generalization of classical $M$-ideals, ideals in operator algebras, and aspects of the theory of Hilbert $C^*$-modules and their maps. Here we give a…
We define a new type of ideal basis called the proper basis that improves both Gr\"obner basis and Buchberger's algorithm. Let $x_1$ be the least variable of a monomial ordering in a polynomial ring $K[x_1,\dotsc,x_n]$ over a field $K$. The…
We show that one can formulate an algebra with lattice ordering so as to contain one quantum and five classical operations as opposed to the standard formulation of the Hilbert space subspace algebra. The standard orthomodular lattice is…
In this paper we propose a new parallel algorithm for solving global optimization (GO) multidimensional problems. The method unifies two powerful approaches for accelerating the search: parallel computations and local tuning on the behavior…