Related papers: Linear Programming in Isabelle/HOL
We extend a semantic verification framework for hybrid systems with the Isabelle/HOL proof assistant by an algebraic model for hybrid program stores, a shallow expression model for hybrid programs and their correctness specifications, and…
This paper presents the first study of the complexity of the optimization problem for integer linear-exponential programs which extend classical integer linear programs with the exponential function $x \mapsto 2^x$ and the remainder…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
We present a trustworthy connection between the Leon verification system and the Isabelle proof assistant. Leon is a system for verifying functional Scala programs. It uses a variety of automated theorem provers (ATPs) to check verification…
We present a formalization of higher-order logic in the Isabelle proof assistant, building directly on the foundational framework Isabelle/Pure and developed to be as small and readable as possible. It should therefore serve as a good…
Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not…
We study the properties of the constructive linear programing problems. The parameters of linear functions in such problems are constructive real numbers. To solve such a problem is to find the optimal plan with the constructive real number…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
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…
Modern machine learning pipelines are built on numerical algorithms. Reliable numerical methods are thus a prerequisite for trustworthy machine learning and cyber-physical systems. Therefore, we contribute a framework for verified numerical…
Mission-time Linear Temporal Logic (MLTL) is rapidly increasing in popularity as a specification logic, e.g., for runtime verification and model checking, driving a need for a trustworthy tool base for analyzing MLTL. In this work, we…
The Isabelle proof assistant includes a small functional language, which allows users to write and reason about programs. So far, these programs could be extracted into a number of functional languages: Standard ML, OCaml, Scala, and…
Linear programming is the seminal optimization problem that has spawned and grown into today's rich and diverse optimization modeling and algorithmic landscape. This article provides an overview of the recent development of first-order…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…
We revisit the linear programming approach to deterministic, continuous time, infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure…
Quantum Hoare Logic (QHL) was introduced in Ying's work to specify and reason about quantum programs. In this paper, we implement a theorem prover for QHL based on Isabelle/HOL. By applying the theorem prover, verifying a quantum program…
Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search,…
We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…