Digitalization of a Family of Multilinear Programming Problems

We consider a class of models in which the constraint equations are described by multilinear functions. To describe this class of models, we use the matrix form for describing a multilinear model, previously introduced by the authors. We introduce the concept of a universal description of a multilinear model. This allows nonprogrammers to quickly perform structural modifications to multilinear models using an on-screen editor. Within the framework of the constructed formalism, the problem of embedding the set of admissible coordinate values of a multilinear model into a linear polyhedron is solved. This allows for obtaining upper bounds for the criteria of multilinear optimization problems. The inverse problem of embedding a linear polyhedron into the set of admissible coordinates of a multilinear model is also considered. If it is possible to embed a linear polyhedron into the admissible set of a multilinear problem, this makes it possible to use linear programming algorithms to solve such problems. The latter have undeniable advantages over multilinear programming algorithms. The obtained results are illustrated with examples.