Related papers: Dyadic linear programming and extensions
In semidefinite programming the dual may fail to attain its optimal value and there could be a duality gap, i.e., the primal and dual optimal values may differ. In a striking paper, Ramana proposed a polynomial size extended dual that does…
Classical existence theorems and solution methods for quadratic programming traditionally rely on the analytical properties of real numbers, specifically compactness and completeness. These tools are unavailable in general linearly ordered…
A method of constructing finite $p$-adic Sylvester expansions for all rationals is presented. This method parallels the classical Fibonacci-Sylvester (greedy) algorithm by iterating a $p$-adic division algorithm. The method extends to…
A fundamental theorem of linear programming states that a feasible linear program is solvable if and only if its objective function is copositive with respect to the recession cone of its feasible set. This paper demonstrates that this…
We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and…
Binary quadratic Diophantine equations are of interest from the viewpoint of computational complexity theory. They contain as special cases many examples of natural problems apparantly occupying intermediate stages in the P-NP hierarchy,…
Integer programs (IPs) on constraint matrices with bounded subdeterminants are conjectured to be solvable in polynomial time. We give a strongly polynomial time algorithm to solve IPs where the constraint matrix has bounded subdeterminants…
The dyadic representation of any singular integral operator, as an average of dyadic model operators, has found many applications. While for many purposes it is enough to have such a representation for a "suitable class" of test functions,…
The problem of optimization of the array size for modern discrete Fourier transform libraries is considered and reformulated as an integer linear programming problem. Acceleration of finding an optimal solution using standard freely…
We produce an infinite family of transcendental numbers which, when raised to their own power, become rational. We extend the method, to investigate positive rational solutions to the equation $x^x = \alpha$, where $\alpha$ is a fixed…
We show that, if an integer sequence is given by a linear recurrence of constant rational coefficients, then it can be represented as the difference of two arithmetic terms with exponentiation, which do not contain any irrational constant.…
Classical primal-dual affine programming takes place over finite dimensional real vector spaces. This results in beautiful duality theory, connecting the optimal solu- tions of the primal maximization problem and the dual minimization…
When $A$ and $B$ are subsets of the integers in $[1,X]$ and $[1,Y]$ respectively, with $|A| \geq \alpha X$ and $|B| \geq \beta X$, we show that the number of rational numbers expressible as $a/b$ with $(a,b)$ in $A \times B$ is $\gg (\alpha…
Computational interpretations of linear logic allow static control of memory resources: the data produced by the program are endowed through its type with attributes that determine its life cycle, and guarantee safe deallocation. The use of…
A rectangle blanket is a set of non-overlapping axis-aligned rectangles, used to approximately represent the two dimensional image of a shape approximately. The use of a rectangle blanket is a widely considered strategy for speeding-up the…
The aim of this paper is a quantitative analysis of the solution set of a system of polynomial nonlinear differential equations, both in the ordinary and partial case. Therefore, we introduce the differential counting polynomial, a common…
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…
Triangulation of a three-dimensional point from at least two noisy 2-D images can be formulated as a quadratically constrained quadratic program. We propose an algorithm to extract candidate solutions to this problem from its semidefinite…
An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…
$p$-adic continued fractions, as an extension of the classical concept of classical continued fractions to the realm of $p$-adic numbers, offering a novel perspective on number representation and approximation. While numerous $p$-adic…