  The advancement of domain reduction techniques has significantly enhanced the
performance of solvers in mathematical programming. This paper delves into the
impact of integrating convexification and domain reduction techniques within
the Outer- Approximation method. We propose a refined convexification-based
Outer-Approximation method alongside a Branch-and-Bound method for both convex
and nonconvex Mixed-Integer Nonlinear Programming problems. These methods have
been developed and incorporated into the open-source Mixed-Integer Nonlinear
Decomposition Toolbox for Pyomo-MindtPy. Comprehensive benchmark tests were
conducted, validating the effectiveness and reliability of our proposed
algorithms. These tests highlight the improvements achieved by incorporating
convexification and domain reduction techniques into the Outer-Approximation
and Branch-and-Bound methods.
