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On the convergence of a new hybrid projection algorithm
  • 时间：0
  • 分类：O175.29[理学—数学;理学—基础数学]
  • 作者机构：[1]曲阜师范大学运筹与管理学院,曲阜273165, [2]上海大学数学系,上海200444
  • 相关基金：国家自然科学基金（10571106和10571116）,曲阜师范大学科研启动基金资助项目.
  • 相关项目：广义半无限规划的理论与算法研究
关键词： 可行点, 罚函数, 精确罚函数, Mangasarian—Fromovitz约束条件, feasible point, penalty function, exact penalty function, Mangasarian-Fromovitz constraint qualification
中文摘要：

本文对可微非线性规划问题提出了一个渐近算法,它是基于一类逼近l1精确罚函数的罚函数而提出的,我们证明了算法所得的极小点列的聚点均为原问题的最优解,并在Mangasarian-Fromovitz约束条件下,证明了有限次迭代之后,所有迭代均为可行的,即迭代所得的极小点为可行点.

英文摘要：

In this paper, we study the asymptotic behavior of methods based on a family of penalty functions that approximate asymptotically the usual exact penalty function for the differentiable nonlinear programming problem. We prove that the minimizer sequence generated by the algorithm is bounded, and its accumulation points are optimal solutions of primal problem. We show that for problems satisfying the Mangasarian-Fromovitz constraint qualification all iterates will remain feasible after a finite number of iterations.

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