针对目标函数中包含耦合函数H(x,y)的非凸非光滑极小化问题,提出了一种线性惯性交替乘子方向法(Linear Inertial Alternating Direction Method of Multipliers,LIADMM)。为了方便子问题的求解,对目标函数中的耦合函数H(x,y)进行线性化...针对目标函数中包含耦合函数H(x,y)的非凸非光滑极小化问题,提出了一种线性惯性交替乘子方向法(Linear Inertial Alternating Direction Method of Multipliers,LIADMM)。为了方便子问题的求解,对目标函数中的耦合函数H(x,y)进行线性化处理,并在x-子问题中引入惯性效应。在适当的假设条件下,建立了算法的全局收敛性;同时引入满足Kurdyka-Lojasiewicz不等式的辅助函数,验证了算法的强收敛性。通过两个数值实验表明,引入惯性效应的算法比没有惯性效应的算法收敛性能更好。展开更多
Ⅰ. INTRODUCTIONIsotopic frequency shifts of vibrational frequencies of polyatomic molecules bring much benefit to the determination of force field constants. There are a variety of isotopic substitution rules for mol...Ⅰ. INTRODUCTIONIsotopic frequency shifts of vibrational frequencies of polyatomic molecules bring much benefit to the determination of force field constants. There are a variety of isotopic substitution rules for molecular vibrational fundamental frequencies, all of which are based on the GF matrix method, that is, with small vibrational amplitude approximation. For X-H(X=C, N, O, S, etc.) stretching vibrations with large anharmonicity, we discover at least展开更多
文摘针对目标函数中包含耦合函数H(x,y)的非凸非光滑极小化问题,提出了一种线性惯性交替乘子方向法(Linear Inertial Alternating Direction Method of Multipliers,LIADMM)。为了方便子问题的求解,对目标函数中的耦合函数H(x,y)进行线性化处理,并在x-子问题中引入惯性效应。在适当的假设条件下,建立了算法的全局收敛性;同时引入满足Kurdyka-Lojasiewicz不等式的辅助函数,验证了算法的强收敛性。通过两个数值实验表明,引入惯性效应的算法比没有惯性效应的算法收敛性能更好。
基金Project supported by the National Natural Science Foundation of China.
文摘Ⅰ. INTRODUCTIONIsotopic frequency shifts of vibrational frequencies of polyatomic molecules bring much benefit to the determination of force field constants. There are a variety of isotopic substitution rules for molecular vibrational fundamental frequencies, all of which are based on the GF matrix method, that is, with small vibrational amplitude approximation. For X-H(X=C, N, O, S, etc.) stretching vibrations with large anharmonicity, we discover at least
