Related papers: A formalization of convex polyhedra based on the s…
We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms…
This paper presents a novel approach for the differentiable rendering of convex polyhedra, addressing the limitations of recent methods that rely on implicit field supervision. Our technique introduces a strategy that combines…
We propose a generalization of the method of cyclic projections, which uses the lengths of projection steps carried out in the past to learn about the geometry of the problem and decides on this basis which projections to carry out in the…
Spectrahedra are linear sections of the cone of positive semidefinite matrices that, as convex bodies, generalize the class of polyhedra. In this paper we investigate the problem of recognizing when a spectrahedron is polyhedral. We reprove…
We present a method for solving the general mixed constrained convex quadratic programming problem using an active set method on the dual problem. The approach is similar to existing active set methods, but we present a new way of solving…
While teaching untyped $\lambda$-calculus to undergraduate students, we were wondering why $\alpha$-equivalence is not directly inductively defined. In this paper, we demonstrate that this is indeed feasible. Specifically, we provide a…
Current approaches for formal verification of algorithms face important limitations. For specification, they cannot express algorithms naturally and concisely, especially for algorithms with states and flexible control flow. For…
We present a Coq formalization of the Quantified Reflection Calculus with one modality, or $\mathsf{QRC}_1$. This is a decidable, strictly positive, and quantified modal logic previously studied for its applications in proof theory. The…
Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the…
This notes explains how standard algorithms that construct sorting networks have been formalised and proved correct in the Coq proof assistant using the SSReflect extension.
Theory of choreographic languages typically includes a number of complex results that are proved by structural induction. The high number of cases and the subtle details in some of them lead to long reviewing processes, and occasionally to…
We provide a simple and efficient algorithm for computing the Euclidean projection of a point onto the capped simplex---a simplex with an additional uniform bound on each coordinate---together with an elementary proof. Both the MATLAB and…
This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary,…
A multi-convex optimization problem is one in which the variables can be partitioned into sets over which the problem is convex when the other variables are fixed. Multi-convex problems are generally solved approximately using variations on…
We describe the implementation of a subfield of the field of formal Puiseux series in polymake. This is employed for solving linear programs and computing convex hulls depending on a real parameter. Moreover, this approach is also useful…
This paper is an introduction to Coxeter polyhedra in spherical, Euclidean, and hyperbolic geometries. It consists of essentially two parts that could be read independently. In the first we introduce non-obtuse polyhedra in the spherical,…
This is a chapter (planned to appear in Wiley's upcoming Encyclopedia of Operations Research and Management Science) describing parts of the theory of convex polyhedra that are particularly important for optimization. The topics include…
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
Computational reflection allows us to turn verified decision procedures into efficient automated reasoning tools in proof assistants. The typical applications of such methodology include mathematical structures that have decidable theory…
In mathematics, it is common practice to have several constructions for the same objects. Mathematicians will identify them modulo isomorphism and will not worry later on which construction they use, as theorems proved for one construction…