运筹学学报
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高雷阜1,* 张亚红1
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教育部高校博士学科科研基金联合资助(No. 20132121110009), 辽宁省教育厅辽宁省高等学校基本科研项目(No. LJ2017QL031), 辽宁省博士启动基金(20170520075)
GAO Leifu1,* ZHANG Yahong1
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摘要：
利用欧几里德若当代数技术，在单调的条件下，用内积的方法证明了对称锥互补问题的一类FB互补函数相应的势函数的水平集有界性. 该方法在理论和应用上相较于以往用迹不等式证明势函数水平集有界性更具普适性和推广价值. 在设计算法求解势函数的无约束极小化问题时，水平集有界性是保证下降算法收敛的重要条件，因此，对算法的设计具有理论意义.
关键词: 对称锥互补问题, FB互补函数, 欧几里德若当代数, 水平集有界
Abstract:
With Euclidean Jordan algebras, we proved the level-boundedness of the merit function related to a penalized Fischer-Burmeister function for symmetric cone complementarity problems with monotonicity in a method of inner product.The method has more universality and promotion value both on theories and applications compared with previous trace inequality method to prove level-boundedness of the merit function. Level-boundedness plays an important part on a guarantee of decline algorithm convergence when we design algorithm to solve unconstrained minimization problem. Therefore, it has theoretical significance on the design of algorithm.
Key words: symmetric cone complementarity problem, Fischer-Burmeister complementarity function, Euclidean Jordan algebras, level-boundedness
高雷阜, 张亚红. 对称锥互补问题的一类惩罚FB函数[J]. 运筹学学报, doi: 10.15960/j.cnki.issn.1007-6093.2018.03.013.
GAO Leifu, ZHANG Yahong. A penalized FB function for symmetric cone complementarity problems[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2018.03.013.
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链接本文: https://www.ort.shu.edu.cn/CN/10.15960/j.cnki.issn.1007-6093.2018.03.013
https://www.ort.shu.edu.cn/CN/Y2018/V22/I3/125
