In topological vector spaces, we estalish a Lagrange Multiplier Theorem forproper efficiency of nonconvex vector opti mization problems. The saddle point theoremsfor the scalar-valued Lagrangian fonction are derived. ...In topological vector spaces, we estalish a Lagrange Multiplier Theorem forproper efficiency of nonconvex vector opti mization problems. The saddle point theoremsfor the scalar-valued Lagrangian fonction are derived. A new duality form is introducedand the duality theorems are established.展开更多
Blind source extraction （BSE） is widely used to solve signal mixture problems where there are only a few desired signals. To improve signal extraction performance and expand its application, we develop an adaptive B...Blind source extraction （BSE） is widely used to solve signal mixture problems where there are only a few desired signals. To improve signal extraction performance and expand its application, we develop an adaptive BSE algorithm with an additive noise model. We first present an improved normalized kurtosis as an objective function, which caters for the effect of noise. By combining the objective function and Lagrange multiplier method, we further propose a robust algorithm that can extract the desired signal as the first output signal. Simulations on both synthetic and real biomedical signals demonstrate that such combination improves the extrac- tion performance and has better robustness to the estimation error of normalized kurtosis value in the presence of noise.展开更多
文摘In topological vector spaces, we estalish a Lagrange Multiplier Theorem forproper efficiency of nonconvex vector opti mization problems. The saddle point theoremsfor the scalar-valued Lagrangian fonction are derived. A new duality form is introducedand the duality theorems are established.
文摘Blind source extraction （BSE） is widely used to solve signal mixture problems where there are only a few desired signals. To improve signal extraction performance and expand its application, we develop an adaptive BSE algorithm with an additive noise model. We first present an improved normalized kurtosis as an objective function, which caters for the effect of noise. By combining the objective function and Lagrange multiplier method, we further propose a robust algorithm that can extract the desired signal as the first output signal. Simulations on both synthetic and real biomedical signals demonstrate that such combination improves the extrac- tion performance and has better robustness to the estimation error of normalized kurtosis value in the presence of noise.
