Formalised completeness proof for the Isabelle/HOL linear programming solver

Establish a formalised completeness proof in Isabelle/HOL for the linear programming solver algorithm that reduces optimisation to a combined constraint satisfaction problem (constructed from the primal and dual constraints and solved via the general simplex algorithm), demonstrating that whenever a linear program has a solution, the algorithm returns an optimal solution.

Background

The paper presents an Isabelle/HOL formalisation of a solver for linear programs that leverages the weak duality theorem and reduces optimisation to a constraint satisfaction problem solvable by an existing general simplex implementation. The authors formally prove soundness of the algorithm and generate executable code via Isabelle’s code generation facilities.

While an informal completeness argument is sketched—asserting that the added constraint preserves optimal solutions and thus the solver finds a solution when one exists—the authors state that a full formalised completeness proof within Isabelle/HOL is currently absent and left for future work.