Exploiting the Black-Litterman framework through error-correction neural networks

Mourtas, Spyridon D.; Katsikis, Vasilios N.

doi:10.1016/j.neucom.2022.05.036

Cited by 22 publications

(4 citation statements)

References 34 publications

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“…Our numerical experience shows that the neutrosophic parameter Ϝ " is particularly efficient as an additional step size composed with previously defined parameters. Additional research can focus on neural network optimization (Mourtas & Katsikis, 2022b) or even portfolio optimization problems (Mourtas & Katsikis, 2022a).…”

Section: Discussionmentioning

confidence: 99%

Neutrosophy in Unconstrained Nonlinear Optimization

Stanimirović¹

2023

European Proceedings of Computers and Technology

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Determining the step length in iterations of nonlinear minimization represents a problem that is not uniquely defined. Motivated by such uncertainty in defining step length, our intention was to use the capabilities of neutrosophy in this process. Our idea is to unify the usability and numerous applications of neutrosophic logic and the enormous importance of nonlinear optimization. An improvement of line search iteration for solving unconstrained optimization is proposed using appropriately defined Neutrosophic logic system in determining appropriate step size for the class of descent direction methods. The basic idea is to use an additional parameter that would monitor the behavior of the objective function and, based on that, correct the step length in known optimization methods. Mutual comparison and analysis of generated numerical results reveal better results generated by the suggested iterations compared to analogous available iterations considering the statistical ranking technique. Statistical measures show advantages of fuzzy improvements of considered line search optimization methods.

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Section: Discussionmentioning

confidence: 99%

Neutrosophy in Unconstrained Nonlinear Optimization

Stanimirović¹

2023

European Proceedings of Computers and Technology

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“…Today their use has expanded to include the resolution of generalized inversion issues, including time-varying Drazin inverse [33], time-varying ML-weighted pseudoinverse [34], time-varying outer inverse [35], time-varying pseudoinverse [36], and core and core-EP inverse [37]. Their use has expanded to include the resolution of linear programming tasks [38], quadratic programming tasks [39,40], systems of nonlinear equations [41,42], and systems of linear equations [43,44]. The creation of a ZNN model typically involves two fundamental steps.…”

Section: Introductionmentioning

confidence: 99%

Towards Higher-Order Zeroing Neural Networks for Calculating Quaternion Matrix Inverse with Application to Robotic Motion Tracking

et al. 2023

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The efficient solution of the time-varying quaternion matrix inverse (TVQ-INV) is a challenging but crucial topic due to the significance of quaternions in many disciplines, including physics, engineering, and computer science. The main goal of this research is to employ the higher-order zeroing neural network (HZNN) strategy to address the TVQ-INV problem. HZNN is a family of zeroing neural network models that correlates to the hyperpower family of iterative methods with adjustable convergence order. Particularly, three novel HZNN models are created in order to solve the TVQ-INV both directly in the quaternion domain and indirectly in the complex and real domains. The noise-handling version of these models is also presented, and the performance of these models under various types of noises is theoretically and numerically tested. The effectiveness and practicality of these models are further supported by their use in robotic motion tracking. According to the principal results, each of these six models can solve the TVQ-INV effectively, and the HZNN strategy offers a faster convergence rate than the conventional zeroing neural network strategy.

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“…Dynamical systems for computing time-varying pseudoinverses were among their subsequent applications [34,35]. Nonlinear equation systems [36,37], linear equation systems [38,39], linear/quadratic programming [40][41][42], and generalized inversion [43,44] are among the challenges that they are currently utilized for. A ZNN model is typically constructed via two primary steps.…”

Section: Introductionmentioning

confidence: 99%

Hermitian Solutions of the Quaternion Algebraic Riccati Equations through Zeroing Neural Networks with Application to Quadrotor Control

Jerbi,

Alshammari,

Aoun

et al. 2023

Mathematics

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The stability of nonlinear systems in the control domain has been extensively studied using different versions of the algebraic Riccati equation (ARE). This leads to the focus of this work: the search for the time-varying quaternion ARE (TQARE) Hermitian solution. The zeroing neural network (ZNN) method, which has shown significant success at solving time-varying problems, is used to do this. We present a novel ZNN model called ’ZQ-ARE’ that effectively solves the TQARE by finding only Hermitian solutions. The model works quite effectively, as demonstrated by one application to quadrotor control and three simulation tests. Specifically, in three simulation tests, the ZQ-ARE model finds the TQARE Hermitian solution under various initial conditions, and we also demonstrate that the convergence rate of the solution can be adjusted. Furthermore, we show that adapting the ZQ-ARE solution to the state-dependent Riccati equation (SDRE) technique stabilizes a quadrotor’s flight control system faster than the traditional differential-algebraic Riccati equation solution.

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Exploiting the Black-Litterman framework through error-correction neural networks

Cited by 22 publications

References 34 publications

Neutrosophy in Unconstrained Nonlinear Optimization

Neutrosophy in Unconstrained Nonlinear Optimization

Towards Higher-Order Zeroing Neural Networks for Calculating Quaternion Matrix Inverse with Application to Robotic Motion Tracking

Hermitian Solutions of the Quaternion Algebraic Riccati Equations through Zeroing Neural Networks with Application to Quadrotor Control

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