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Exactness and algorithm of an objective penalty function

机译：目标罚函数的精确度和算法

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Penalty function is an important tool in solving many constrained optimization problems in areas such as industrial design and management. In this paper, we study exactness and algorithm of an objective penalty function for inequality constrained optimization. In terms of exactness, this objective penalty function is at least as good as traditional exact penalty functions. Especially, in the case of a global solution, the exactness of the proposed objective penalty function shows a significant advantage. The sufficient and necessary stability condition used to determine whether the objective penalty function is exact for a global solution is proved. Based on the objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions. Furthermore, the sufficient and necessary calmness condition on the exactness of the objective penalty function is proved for a local solution. An algorithm is presented in the paper in finding a local solution, with its convergence proved under some conditions. Finally, numerical experiments show that a satisfactory approximate optimal solution can be obtained by the proposed algorithm.
机译：罚函数是解决工业设计和管理等领域中许多受限优化问题的重要工具。在本文中，我们研究了不等式约束优化的目标惩罚函数的准确性和算法。在准确性方面，该客观惩罚函数至少与传统的精确惩罚函数一样好。特别是在整体解决方案的情况下，提出的目标惩罚函数的准确性显示出显着的优势。证明了用于确定目标罚函数对于全局解是否精确的充分必要条件。基于目标惩罚函数，开发了一种求解不等式约束优化问题的全局解的算法，并在一定条件下证明了其全局收敛性。此外，证明了局部罚函数的正确性的充要条件。本文提出了一种寻找局部解的算法，并在一定条件下证明了其收敛性。最后，数值实验表明，该算法可以得到令人满意的近似最优解。

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