3D Malfatti's constrained optimization problem

In 1803, the Italian mathematician Malfatti posed a problem of packing three non-overlapping circles of maximum total area within a given triangle. Malfatti initially believed that the optimal solution involved three circles inscribed within the triangle, each tangent to the other two and touching two sides of the triangle. However, it is now widely recognized that this solution is not optimal. The problem for the first time was formulated as a global optimization problem in [9]. In this paper, we introduce a new formulation of Malfatti's problem, referred to as the 3D Malfatti`s constrained optimization problem in three-dimensional space. The problem is presented as a nonconvex optimization problem with nonlinear constraints, and numerical experiments were conducted using Python for various cases.