Related papers: Programmation Lin\'eaire, une nouvelle approche / …
A typical way in which a machine acquires knowledge from humans is by programming. Compared to learning from demonstrations or experiences, programmatic learning allows the machine to acquire a novel skill as soon as the program is written,…
A key challenge in program synthesis is the astronomical size of the search space the synthesizer has to explore. In response to this challenge, recent work proposed to guide synthesis using learned probabilistic models. Obtaining such a…
Many industrial applications require finding solutions to challenging combinatorial problems. Efficient elimination of symmetric solution candidates is one of the key enablers for high-performance solving. However, existing model-based…
Code super-optimization is the task of transforming any given program to a more efficient version while preserving its input-output behaviour. In some sense, it is similar to the paraphrase problem from natural language processing where the…
Several different ways exist for approaching hard optimization problems. Mathematical programming techniques, including (integer) linear programming-based methods and metaheuristic approaches, are two highly successful streams for…
We explicate a procedure to solve general linear differential equations, which connects the desired solutions to monomials x^m of an appropriate degree m. In the process the underlying symmetry of the equations under study, as well as that…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
As the dimension of a system increases, traditional methods for control and differential games rapidly become intractable, making the design of safe autonomous agents challenging in complex or team settings. Deep-learning approaches avoid…
We give new proofs of asymptotic upper bounds of coding theory obtained within the frame of Delsarte's linear programming method. The proofs rely on the analysis of eigenvectors of some finite-dimensional operators related to orthogonal…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
We present a conceptually simple yet effective algorithm to detect wireframes in a given image. Compared to the previous methods which first predict an intermediate heat map and then extract straight lines with heuristic algorithms, our…
In this paper we develop a very special substitution method for solving a general linear programming problem (LPP). Of course the substitution is a kind of elimination of variable but this method must not be confused with the so-called…
Inspired by the linear programming method developed by Cohn and Elkies (Ann. Math. 157(2): 689-714, 2003), we introduce a new linear programming method to solve the sphere packing problem. More concretely, we consider sequences of auxiliary…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
This paper introduces new algorithm for line extraction from laser range data including methodology for efficient computation. The task is cast to series of one dimensional problems in various spaces. A fast and simple specialization of…
It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular…
Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…