基数约束优化问题的内罚函数法
An Interior Penalty Algorithm for Cardinality-Constrained Optimization Problems
摘要: 基数约束优化问题是一类重要的优化问题，这类问题在很多领域都有着广泛的应用。由于其具有较难处理的基数约束，所以对基数约束优化问题的算法研究较少。本文将介绍基数约束优化问题的内罚函数法，并证明了该算法产生点列收敛到AM-稳定点。进一步证明在AM-正则性条件下，可以得到基数约束优化问题的M-稳定点。
Abstract: The cardinality-constrained optimization problems are an important class of optimization problems which have been applied in many fields. Due to the special structure of the cardinality constraints, there are few researches on the algorithm of cardinality-constraint optimization problems. We in-troduce an interior penalty algorithm for cardinality-constrained optimization problems and prove that the algorithm reaches an approximate Mordukhovich stationary. Furthermore, under the AM-regularity condition, we can obtain the Mordukhovich stationary of cardinality-constrained op-timization problems.
文章引用：吴霜, 王雪纯. 基数约束优化问题的内罚函数法[J]. 应用数学进展, 2024, 13(1): 21-28. https://doi.org/10.12677/AAM.2024.131003

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