Malfatti’s constrained optimization problem

Abstract

In 1803 Italian mathematician Malfatti posed the following problem how to pack three non-overlapping circles of maximum total area in a given triangle. Malfatti originally assumed that the solution to this problem are three circles inscribed in a triangle such that each circle tangent to other two and touches two sides of the triangle. Now it is well known that Malfatti’s solution is not optimal. The problem for the first time was treated as a global optimization problem in Enkhbat [9]. In this paper, we consider a new formulation of Malfatti’s problem called Malfatti’s constrained optimization problem. The new problem is formulated as a nonconvex optimization problem with nonlinear constraints. Numerical experiments were conducted on Python for the cases.