Theoretic Background of Computer Solution of Combinatorial and Geometric Configuration Problems

We develop theoretical foundations for computer solving configuration theory problems using general-purpose nonlinear programming solvers. The problems related to the existence and isomorphism of combinatorial and geometric configurations on a plane are formulated as continuous nonlinear programs. It is done with the help of continuous functional representations of different Boolean sets. The computer experiment is designed where the continuous optimization and feasibility formulation are utilized and IPOPT solver implemented in the Python package Gekko is applied.