Global Sufficient Conditions for Nonconvex Cubic Minimization Problem with Box Constraints

In this paper, we focus on deriving some sufficient conditions for global solutions to cubic minimization problems with box constraints. Our main tool is an extension of the global subdifferential, L-normal cone approach, developed by Jeyakumar et al. (J. Glob. Optim., 2007; Math. Program. Ser. A 110, 2007), and underestimator functions. By applying these tools to characteristic global solutions, we provide some sufficient conditions for cubic programming problem with box constraints. An example is given to demonstrate that the sufficient conditions can be used effectively for identifying global minimizers of certain cubic minimization problems with box constraints.