Related papers: Elimination via saturation
The analysis of large datasets is often complicated by the presence of missing entries, mainly because most of the current machine learning algorithms are designed to work with full data. The main focus of this work is to introduce a…
Whitney's broken circuit theorem gives a graphical example to reduce the number of the terms in the sum of the inclusion-exclusion formula by a predicted cancellation. So far, the known cancellations for the formula strongly depend on the…
Compressing resource-intensive large language models by removing whole transformer blocks is a seemingly simple idea, but identifying which blocks to remove constitutes an exponentially difficult combinatorial problem. In this paper, we…
It is shown that any set of nonzero monomial prime ideals can be realized as the stable set of associated prime ideals of a monomial ideal. Moreover, an algorithm is given to compute the stable set of associated prime ideals of a monomial…
Second-order quantifier-elimination is the problem of finding, given a formula with second-order quantifiers, a logically equivalent first-order formula. While such formulas are not computable in general, there are practical algorithms and…
An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…
A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation…
We prove in this work that the well-known lasso problem can be solved exactly without homotopy using novel differential inclusions techniques. Specifically, we show that a selection principle from the theory of differential inclusions…
Upper bound limit analysis allows one to evaluate directly the ultimate load of structures without performing a cumbersome incremental analysis. In order to numerically apply this method to thin plates in bending, several authors have…
We study an abstract setting for cutting planes for integer programming called the infinite group problem. In this abstraction, cutting planes are computed via cut generating function that act on the simplex tableau. In this function space,…
We describe different optimization techniques to perform the assembly of finite element matrices in Matlab and Octave, from the standard approach to recent vectorized ones, without any low level language used. We finally obtain a simple and…
Inversion of sparse matrices with standard direct solve schemes is robust, but computationally expensive. Iterative solvers, on the other hand, demonstrate better scalability; but, need to be used with an appropriate preconditioner (e.g.,…
In this paper, we propose a new method for removing all the redundant inequalities generated by Fourier-Motzkin elimination. This method is based on an improved version of Balas' work and can also be used to remove all the redundant…
An algorithm for resolution of singularities in characteristic zero is described. It is expressed in terms of multi-ideals, that essentially are defined as a finite sequence of pairs, each one consiting of a sheaf of ideals and a positive…
In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…
This paper describes a general framework for automatic termination analysis of logic programs, where we understand by ``termination'' the finitenes s of the LD-tree constructed for the program and a given query. A general property of…
We describe a new quantifier elimination algorithm for real closed fields based on Thom encoding and sign determination. The complexity of this algorithm is elementary recursive and its proof of correctness is completely algebraic. In…
The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is \emph{strong homogeneity}…
View materialization, index selection, and plan caching are well-known techniques for optimization of query processing in database systems. The essence of these tasks is to select and save a subset of the most useful candidates…
When a black-box optimization objective can only be evaluated with costly or noisy measurements, most standard optimization algorithms are unsuited to find the optimal solution. Specialized algorithms that deal with exactly this situation…