Related papers: Automatic Solver Generator for Systems of Laurent …
Mathematical optimization is ubiquitous in modern applications. However, in practice, we often need to use nonlinear optimization models, for which the existing optimization tools such as Cplex or Gurobi may not be directly applicable and…
An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as…
Symmetry in integer programming causes redundant search and is often handled with symmetry breaking constraints that remove as many equivalent solutions as possible. We propose an algebraic method which allows to generate a random family of…
Holographic algorithms introduced by Valiant are composed of two ingredients: matchgates, which are gadgets realizing local constraint functions by weighted planar perfect matchings, and holographic reductions, which show equivalences among…
We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and…
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…
Finding relative pose between two calibrated images is a fundamental task in computer vision. Given five point correspondences, the classical five-point methods can be used to calculate the essential matrix efficiently. For the case of $N$…
The Euler-Poincar\'e (EP) equations describe the geodesic motion on the diffeomorphism group. For template matching (template deformation), the Euler-Lagrangian equation, arising from minimizing an energy function, falls into the…
We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on…
We propose a method called ideal regression for approximating an arbitrary system of polynomial equations by a system of a particular type. Using techniques from approximate computational algebraic geometry, we show how we can solve ideal…
We give the first exact determinantal formula for the resultant of an unmixed sparse system of four Laurent polynomials in three variables with arbitrary support. This follows earlier work by the author on exact formulas for bivariate…
We provide an algorithm that takes as an input a given parametric family of homogeneous polynomials, which is invariant under the action of the general linear group, and an integer $d$. It outputs the ideal of that family intersected with…
In recent years it has been shown that for many linear algebra operations it is possible to create families of algorithms following a very systematic procedure. We do not refer to the fine tuning of a known algorithm, but to a methodology…
The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…
Many computer vision applications require robust and efficient estimation of camera geometry. The robust estimation is usually based on solving camera geometry problems from a minimal number of input data measurements, i.e., solving minimal…
Solving math word problems is a challenging task that requires accurate natural language understanding to bridge natural language texts and math expressions. Motivated by the intuition about how human generates the equations given the…
This paper proposes to solve the Total Variation regularized models by finding the residual between the input and the unknown optimal solution. After analyzing a previous method, we developed a new iterative algorithm, named as Residual…
A classical problem in Distance Geometry, with multiple practical applications (in molecular structure determination, sensor network localization etc.) is to find the possible placements of the vertices of a graph with given edge lengths.…