Global sufficient optimality conditions for a special cubic minimization problem
Summary: We present some sufficient global optimality conditions for a special cubic minimization problem with box constraints or binary constraints by extending the global subdifferential approach proposed by \textit{V. Jeyakumar, A. M. Rubinov} and \textit{Z. Y. Wu} [J. Glob. Optim. 36, No.~3, 471--481 (2006; Zbl 1131.90060). The present conditions generalize the results developed in [Zbl 1131.90060] where a quadratic minimization problem with box constraints or binary constraints was considered. In addition, a special diagonal matrix is constructed, which is used to provide a convenient method for justifying the proposed sufficient conditions. Then, the reformulation of the sufficient conditions follows. It is worth noting that this reformulation is also applicable to the quadratic minimization problem with box or binary constraints considered in [Zbl 1131.90060] and \textit{Y. Wang} et al. [J. Glob. Optim. 47, No. 4, 583--595 (2010; Zbl 1228.90088)]. Finally some examples demonstrate that our optimality conditions can effectively be used for identifying global minimizers of the certain nonconvex cubic minimization problem.
scientific article; zbMATH DE number 6173661
scientific article