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摘要
In this paper, we present global optimality conditions for cubic minimization involving box or bivalent constraints via quadratic overestimators and underestimators. We first construct quadratic overestimators and underestimators of cubic function. Then, by utilizing quadratic overestimators, we derive a necessary global optimality condition for cubic minimization problems where the cubic objective function contains no cross terms. Finally, we establish the sufficient condition for global minimizers using quadratic underestimators,and also derive global optimality conditions for cubic minimization over bivalent constraints before we illustrate new optimality conditions by providing examples.
