文章针对概率约束优化问题,提出了一种新颖的特征函数光滑近似方法,该方法利用双曲正切函数来构造近似函数。概率约束优化问题在工程、金融、能源等领域具有广泛的应用,其理论研究与实际应用价值日益凸显。尽管如此,该类问题因其固有的...文章针对概率约束优化问题,提出了一种新颖的特征函数光滑近似方法,该方法利用双曲正切函数来构造近似函数。概率约束优化问题在工程、金融、能源等领域具有广泛的应用,其理论研究与实际应用价值日益凸显。尽管如此,该类问题因其固有的非线性和随机性,使得传统的优化方法在求解时面临计算复杂度高、收敛速度慢等挑战。为了克服这些困难,文章首先对现有的光滑近似方法进行了深入的综述,包括序列凸近似、罚函数法、障碍函数法等,并比较了它们在处理概率约束优化问题时的性能和适用范围。在此基础上,我们提出了一种基于双曲正切函数的光滑近似方法,该方法通过提供更为平滑的近似,显著降低了问题的求解难度,并提高了计算效率。实验结果表明,相比于传统方法,本文提出的方法在保持求解质量的同时,大幅减少了计算时间,为概率约束优化问题的解决提供了新的思路和工具。This paper addresses the probability constraint optimization problem and proposes a novel smooth approximation method for the characteristic function, which utilizes the hyperbolic tangent function to construct the approximation. Probability constraint optimization problems are widely applied in fields such as engineering, finance, and energy, and their theoretical research and practical application value are increasingly prominent. Nevertheless, due to their inherent nonlinearity and randomness, traditional optimization methods face challenges such as high computational complexity and slow convergence speed when solving these problems. To overcome these difficulties, this paper first provides an in-depth review of existing smooth approximation methods, including sequential convex approximation, penalty function methods, and barrier function methods, and compares their performance and applicability in dealing with probability constraint optimization problems. Based on this, we propose a smooth approximation method based on the hyperbolic tangent function, which significantly reduces the difficulty of problem-solving and improves computational efficiency by providing a smoother approximation. Experimental results show that, compared to traditional methods, the method proposed in this paper greatly reduces computation time while maintaining solution quality, offering new insights and tools for solving probability constraint optimization problems.展开更多
文摘文章针对概率约束优化问题,提出了一种新颖的特征函数光滑近似方法,该方法利用双曲正切函数来构造近似函数。概率约束优化问题在工程、金融、能源等领域具有广泛的应用,其理论研究与实际应用价值日益凸显。尽管如此,该类问题因其固有的非线性和随机性,使得传统的优化方法在求解时面临计算复杂度高、收敛速度慢等挑战。为了克服这些困难,文章首先对现有的光滑近似方法进行了深入的综述,包括序列凸近似、罚函数法、障碍函数法等,并比较了它们在处理概率约束优化问题时的性能和适用范围。在此基础上,我们提出了一种基于双曲正切函数的光滑近似方法,该方法通过提供更为平滑的近似,显著降低了问题的求解难度,并提高了计算效率。实验结果表明,相比于传统方法,本文提出的方法在保持求解质量的同时,大幅减少了计算时间,为概率约束优化问题的解决提供了新的思路和工具。This paper addresses the probability constraint optimization problem and proposes a novel smooth approximation method for the characteristic function, which utilizes the hyperbolic tangent function to construct the approximation. Probability constraint optimization problems are widely applied in fields such as engineering, finance, and energy, and their theoretical research and practical application value are increasingly prominent. Nevertheless, due to their inherent nonlinearity and randomness, traditional optimization methods face challenges such as high computational complexity and slow convergence speed when solving these problems. To overcome these difficulties, this paper first provides an in-depth review of existing smooth approximation methods, including sequential convex approximation, penalty function methods, and barrier function methods, and compares their performance and applicability in dealing with probability constraint optimization problems. Based on this, we propose a smooth approximation method based on the hyperbolic tangent function, which significantly reduces the difficulty of problem-solving and improves computational efficiency by providing a smoother approximation. Experimental results show that, compared to traditional methods, the method proposed in this paper greatly reduces computation time while maintaining solution quality, offering new insights and tools for solving probability constraint optimization problems.
