Related papers: Programmation Lin\'eaire, une nouvelle approche / …
We establish a connection between linear codes and hyperplane arrangements using the Thomas decomposition of polynomial systems and the resulting counting polynomial. This yields both a generalization and a refinement of the weight…
We propose a vector linear programming formulation for a non-stationary, finite-horizon Markov decision process with vector-valued rewards. Pareto efficient policies are shown to correspond to efficient solutions of the linear program, and…
We propose a flexible gradient-based framework for learning linear programs from optimal decisions. Linear programs are often specified by hand, using prior knowledge of relevant costs and constraints. In some applications, linear programs…
A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…
A framework is developed for applying accelerated methods to general hyperbolic programming, including linear, second-order cone, and semidefinite programming as special cases. The approach replaces a hyperbolic program with a convex…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
Floor planning is an important and difficult task in architecture. When planning office buildings, rooms that belong to the same organisational unit should be placed close to each other. This leads to the following NP-hard mathematical…
Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…
Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…
Optical computing systems provide an alternate hardware model which appears to be aligned with the demands of neural network workloads. However, the challenge of implementing energy efficient nonlinearities in optics -- a key requirement…
Linear superiorization (abbreviated: LinSup) considers linear programming (LP) problems wherein the constraints as well as the objective function are linear. It allows to steer the iterates of a feasibility-seeking iterative process toward…
In this paper, we introduce methods of encoding propositional logic programs in vector spaces. Interpretations are represented by vectors and programs are represented by matrices. The least model of a definite program is computed by…
Algorithms for solving the linear classification problem have a long history, dating back at least to 1936 with linear discriminant analysis. For linearly separable data, many algorithms can obtain the exact solution to the corresponding…
In today's software world with its cornucopia of reusable software libraries, when a programmer is faced with a programming task that they suspect can be completed through the use of a library, they often look for code examples using a…
Linear Programming is now included in Algorithm undergraduate and postgraduate courses for Computer Science majors. It is possible to teach interior-point methods directly with just minimal knowledge of Algebra and Matrices.
In this work, we explore explicit Large Language Model (LLM)-powered support for the iterative design of computer programs. Program design, like other design activity, is characterized by navigating a space of alternative problem…
In connection with the needs of solving optimization problems, the development of conditional minimization methods with convenient numerical implementation continues to attract the attention of mathematicians. In this monograph we propose…
Predictive coding has emerged as a prominent model of how the brain learns through predictions, anticipating the importance accorded to predictive learning in recent AI architectures such as transformers. Here we propose a new framework for…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…
Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…