摘要
众所周知,在优化问题算法与理论的研究过程中,如增广拉格朗日方法的应用以及优化问题的灵敏性分析等,凸集上投影算子的性质起着极其重要的作用。通过投影算子对应的凸二次优化的Karush-Kuhn-Tucker(KKT)条件,给出了可变盒子集合投影算子显示解的计算方法,并对其Matlab软件实现。通过具体的数值算例,验证了研究结果的正确性与有效性。
As we all know, the properties of the metric projection over convex sets play significant role in the study of the algorithms and theory of the related optimization problems such as the applications of the augmented Lagrangian methods and sensibility analysis of optimization problems, and so on. This paper pres- ents the computational formula of the metric projection over the set of variable box by using the Karush-Ku- hn-Tucker (KKT) condition of the corresponding convex quadratic optimization problems. We implement it via Matlab software. The reported numerical results for specific examples show that our algorithm is correct and effective.
出处
《沈阳航空航天大学学报》
2013年第6期93-96,共4页
Journal of Shenyang Aerospace University
基金
国家自然科学基金青年科学基金(项目编号:11001180
11371255)
教育部留学归国人员科研启动基金(项目编号:JYB201302)
辽宁省高等学校杰出青年学者成长计划(项目编号:LJQ2012012)
关键词
投影算子
可变盒子集合
凸优化
KKT条件
projection operator
the set of variable box
convex optimization
KKT condition.