Can you advise me any kind of existing software that can help to solve the disjunctive programming problem?The problem is the following.We have unit 3D planes $\Pi_{1}, \ldots, \Pi_{N}$ (they are known). Let us write them as follows: $U_{j} x = H_{j}, j = 1, \ldots, N$.Having the fixed numbers $n$ and $m$, we want to find 3D planes $\pi_{1}, \ldots, \pi_{n}$ and 3D points $x_{1}, \ldots, x_{m}$ such that:Planes and points satisfy the incidence structure:$x_{i} \in \pi_{j}\;\;\forall(i, j) \in I$, where $I$ is fixed known set $I \subseteq \{1, \ldots, m\} \times \{1, \ldots, n\}$.The polyhedron bounded by planes $\pi_{1}, \ldots, \pi_{n}$ is convex.and minimize the function $\sum \limits_{j = 1}^{N}(H_{j} - \max \limits_{i = 1, \ldots, m} (x_{i}, U_{j}))^{2}$.Since we have a $\max$ in the functional, the above problem can be formulated as a disjunctive programming program as follows:$$\begin{align}&\text{minimize} \sum \limits_{j = 1}^{N}(H_{j} - L_{j})^{2}\\&\text{subject to } \, (1-2) \text{ and }\forall j = 1, \ldots, N\; \exists i \text{ such that } (x_{i}, U_{j}) = H_{j} \enspace .\end{align}$$I have read from Internet that such problems are called disjunctive programming. Can you give any hint which software can be used to solve it?
Disjunctive programming software
quadratic programming;solver