Global Sufficient Optimality Conditions for a Special Cubic Minimization Problem. (6th September 2012)

• Record Type: Journal Article
• Authors: Zhang, Xiaomei; Wang, Yanjun; Ma, Weimin
• Other Names: Shi Jianming Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2012(2012)
• Publication Date: 2012-09-06
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2012/871741
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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 V. Jeyakumar et al. (2006). The present conditions generalize the results developed in the work of V. Jeyakumar et al. 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 the works of V. Jeyakumar et al. (2006) and Y. Wang et al. (2010). Finally some examples demonstrate that our optimality conditions can effectively be used for identifying global minimizers of the certain nonconvex cubic minimization problem.