相关论文: Computing parametric rational generating functions…
We present alfonso, an open-source Matlab package for solving conic optimization problems over nonsymmetric convex cones. The implementation is based on the authors' corrected analysis of a primal-dual interior-point method of Skajaa and…
In our work, we consider the problem of computing a vector $x \in Z^n$ of minimum $\|\cdot\|_p$-norm such that $a^\top x \not= a_0$, for any vector $(a,a_0)$ from a given subset of $Z^n$ of size $m$. In other words, we search for a vector…
We extend the shell and kernel reductions for hyperexponential functions over the field of rational functions to a monomial extension. Both of the reductions are incorporated into one algorithm. As an application, we present an additive…
The traditional view in numerical conformal mapping is that once the boundary correspondence function has been found, the map and its inverse can be evaluated by contour integrals. We propose that it is much simpler, and 10-1000 times…
Motivated by some algorithmic problems, we give lower bounds on the size of the multiplicative groups containing rational function images of low-dimensional affine subspaces of a finite field~$\mathbb{F}_{q^n}$ considered as a linear space…
We study geometric duality for convex vector optimization problems. For a primal problem with a $q$-dimensional objective space, we formulate a dual problem with a $(q+1)$-dimensional objective space. Consequently, different from an…
We consider a countable tree $T$, possibly having vertices with infinite degree, and an arbitrary stochastic nearest neighbour transition operator $P$. We provide a boundary integral representation for general eigenfunctions of $P$ with…
In this paper, we construct a family of Bernstein functions using a class of rational parametrization. The new family of rational Bernstein basis on an index $\alpha \in {\left(-\infty \, , \, 0 \right)}\cup {\left(1 \, , \,…
In this work we introduce a memory-efficient method for computing the action of a Hermitian matrix function on a vector. Our method consists of a rational Lanczos algorithm combined with a basis compression procedure based on rational…
Regarding quaternions as normal matrices, we first characterize the $2\times 2$ matrix-valued functions, defined on subsets of quaternions, whose values are quaternions. Then we investigate the regularity of quaternionic-valued functions,…
We extend the scope of analytic combinatorics to classes containing objects that have irrational sizes. The generating function for such a class is a power series that admits irrational exponents (which we call a Ribenboim series). A…
We construct a generating functional for the exact evalutation of a coherent representation of spin network amplitudes. This generating functional is defined for arbitrary graphs and depends only on a pair of spinors for each edge. The…
We introduce the notion of rationality for hyperholomorphic functions (functions in the kernel of the Cauchy-Fueter operator). Following the case of one complex variable, we give three equivalent definitions: the first in terms of…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
In this paper, we present the first outer approximation algorithm for multi-objective mixed-integer linear programming problems with any number of objectives. The algorithm also works for certain classes of non-linear programming problems.…
The manuscript studies configurations of non-overlapping non-bonding dominoes on finite rectangular boards of unit squares characterized by row and column number. The non-bonding dominoes are defined here by the requirement that any domino…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
This paper presents generalizations of semidefinite programming formulations of 1-norm optimization problems over infinite dictionaries of vectors of complex exponentials, which were recently proposed for superresolution, gridless…
For a fixed dimension $N$ we compute the generating function of the numbers $t_N(n)$ (respectively $\bar{t}_N(n)$) of $PGL_{N+1}(k)$-orbits of rational $n$-sets (respectively rational $n$-multisets) of the projective space $\mathb{P}^N$…
The main aim of this paper is to provide a unified approach to deriving identities for the Bernstein polynomials using a novel generating function. We derive various functional equations and differential equations using this generating…