Abstract In this paper, we introduce two novel forward-backward splitting algorithms (FBSAs) for nonsmooth convex minimization. We provide a thorough convergence analysis, emphasizing the new algorithms and contrasting them with existing ones. Our findings are validated through a numerical example. The practical utility of these algorithms in real-world applications, including machine learning for tasks such as classification, regression, and image deblurring reveal that these algorithms consistently approach optimal solutions with fewer iterations, highlighting their efficiency in real-world scenarios.

This paper studies the error performance of free-space optical (FSO) systems, employing subcarrier intensity modulation (SIM) with M-ary differential phase-shift keying (MDPSK). Novel analytical expressions for the symbol error probability are derived, based on the Fourier series approach. The irradiance fluctuations of the received optical signal are modeled by considering both Gamma-Gamma atmospheric turbulence and pointing errors. In addition, hardware imperfections of DPSK demodulator, as the phase noise of local oscillator at the receiver, are considered. It is illustrated that the phase noise significantly degrades the system performance, especially when the optical signal transmission is impaired by weak atmospheric turbulence and weak pointing errors effect. Furthermore, the phase noise results in an unrecoverable error-rate floor, which is an important limiting factor for SIM-DPSK FSO systems.

A measure of efficiency of simultaneous methods for determination of polynomial zeros, defined by the coefficient of efficiency, is considered. This coefficient takes into consideration (1) the R-order of convergence in the sense of the definition introduced by Ortega and Rheinboldt (Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York, 1970) and (2) the number of basic arithmetic operations per iteration, taken with certain weights depending on a processor time. The introduced definition of computational efficiency was used for comparison of the simultaneous methods with various structures.