Related papers: Linear Programming in Isabelle/HOL
Integer Linear Programming with $n$ binary variables and $m$ many $0/1$-constraints can be solved in time $2^{\tilde O(m^2)} \text{poly}(n)$ and it is open whether the dependence on $m$ is optimal. Several seemingly unrelated problems,…
We describe SeCaV, a sequent calculus verifier for first-order logic in Isabelle/HOL, and the SeCaV Unshortener, an online tool that expands succinct derivations into the full SeCaV syntax. We leverage the power of Isabelle/HOL as a proof…
This paper considers the problem of maximizing multiple linear functions over the probability simplex. A classification of feasible points is indicated. A necessary and sufficient condition for a member of each class to be an efficient…
Linear Software Models is a systematic effort to formulate a theory of software systems neatly based upon standard mathematics, viz. linear algebra. It has appeared in a series of papers dealing with various aspects of the theory. But one…
In interactive theorem proving, formalization quality is a key factor for maintainability and re-usability of developments and can also impact proof-checking performance. Commonly, anti-patterns that cause quality issues are known to…
The proof of information inequalities and identities under linear constraints on the information measures is an important problem in information theory. For this purpose, ITIP and other variant algorithms have been developed and…
Linearization is the procedure of rewriting a process term into a linear form, which consist only of basic operators of the process language. This procedure is interesting both from a theoretical and a practical point of view. In…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
Integer linear programming (ILP) encompasses a very important class of optimization problems that are of great interest to both academia and industry. Several algorithms are available that attempt to explore the solution space of this class…
Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are…
Clear and concise code is necessary to ensure maintainability, so it is crucial that the software is as simple as possible to understand, to avoid bugs and, above all, vulnerabilities. There are many ways to enhance software without…
Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems. In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the…
Under some mild Markov assumptions it is shown that the problem of designing optimal sequential tests for two simple hypotheses can be formulated as a linear program. The result is derived by investigating the Lagrangian dual of the…
Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, there is a little tool support for transferring this expert knowledge to a wider…
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…
A well motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an…
A sparse linear programming (SLP) problem is a linear programming problem equipped with a sparsity (or cardinality) constraint, which is nonconvex and discontinuous theoretically and generally NP-hard computationally due to the…
Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…
A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used…
We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general…