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This paper is concerned with a covering problem of Euclidean space by a particular arrangement of cones that are not necessarily full and are allowed to overlap. The problem provides an equivalent geometric reformulation of the solvability…
We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of…
A convex relaxation of a quadratically constrained quadratic program (QCQP) is called exact if it has a rank-$1$ optimal solution that corresponds to an optimal solution of the QCQP. Given a QCQP whose convex relaxation is exact, this paper…
Multivariate piecewise polynomial functions (or splines) on polyhedral complexes have been extensively studied over the past decades and find applications in diverse areas of applied mathematics including numerical analysis, approximation…
We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…
Numerical tools for constraints solving are a cornerstone to control verification problems. This is evident by the plethora of research that uses tools like linear and convex programming for the design of control systems. Nevertheless, the…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…
We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer…
We give new positive and negative results (some conditional) on speeding up computational algebraic geometry over the reals: (1) A new and sharper upper bound on the number of connected components of a semialgebraic set. Our bound is novel…
A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of…
We address a specific but recurring problem related to sampled linear systems. In particular, we provide a numerical method for the rigorous verification of constraint satisfaction for linear continuous-time systems between sampling…
Certificates of polynomial nonnegativity can be used to obtain tight dual bounds for polynomial optimization problems. We consider Sums of Nonnegative Circuit (SONC) polynomials certificates, which are well suited for sparse problems since…
In this paper, we propose a constraint-based modeling approach for the problem of discovering frequent gradual patterns in a numerical dataset. This SAT-based declarative approach offers an additional possibility to benefit from the recent…
Deep Learning has become overly complicated and has enjoyed stellar success in solving several classical problems like image classification, object detection, etc. Several methods for explaining these decisions have been proposed. Black-box…
We present an algorithm for the numerical evaluation of elliptic multiple polylogarithms for arbitrary arguments and to arbitrary precision. The cornerstone of our approach is a procedure to obtain a convergent $q$-series representation of…
The constraint satisfaction problem (CSP) on a relational structure B is to decide, given a set of constraints on variables where the relations come from B, whether or not there is a assignment to the variables satisfying all of the…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a…
Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range,…
We propose a cut-free cyclic system for Transitive Closure Logic (TCL) based on a form of hypersequents, suitable for automated reasoning via proof search. We show that previously proposed sequent systems are cut-free incomplete for basic…