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In this paper, a computational method is proposed for solving a class of fractional optimal control problems subject to canonical constraints of equality and inequality. Fractional derivatives are described in the Atangana–Baleanu-Caputo sense, and their fractional orders can be different. To solve this problem, we present a discretization scheme based on the trapezoidal rule and a novel numerical integration technique. Then, the gradient formulas of the cost and constraint functions with respect to the decision variables are derived. Furthermore, a gradient-based optimization algorithm for solving the discretized optimal control problem is developed. Finally, the applicability and effectiveness of the proposed algorithm are verified through three non-trivial example problems. [ABSTRACT FROM AUTHOR]

In this paper, we consider an optimal control problem whose dynamic system consists of control-dependent time-delayed arguments in the control and discrete time-delayed arguments in the state. Recently, control parameterization methods using hybrid time-scale transformation techniques have been developed to optimize both the control parameters and their switching times when the dynamic system consists of discrete time-delayed arguments only. This transformation maps the variable switching times in the original time horizon to fixed switching times in the new time horizon. Thus, the purpose of this paper is to extend the above technique to solve problems with both control-dependent time-delayed arguments and discrete time-delayed arguments. Using the above technique, we convert both the delayed state vector and the delayed control vector into non-delayed vectors in the new time horizon; hence both the control parameters and their switching times can be optimized. The gradients of the objective functions and the constraint functions with respect to the switching times and the controls are obtained. Two numerical examples, one of which is a practical problem involving the optimal transmission of messages in an internet, are solved to demonstrate the efficiency of our method. [ABSTRACT FROM AUTHOR]

• GCM and G-GCM are proposed for solving group square-root Lasso (GSRL) efficiently. Both of them scale well with large problem scale. • The strict descend property and global convergence are proved. • The proposed algorithms can also be used for fast implementation of statistically sound group-sparse regression methods including SPICE/GSPICE and LIKES/BLIKES. A variant for solving Lasso and group Lasso is also provided. Group square-root Lasso (GSRL) is a promising tool for group-sparse regression since the hyperparameter is independent of noise level. Recent works also reveal its connections to some statistically sound and hyperparameter-free methods, e.g., group-sparse iterative covariance-based estimation (GSPICE). However, the non-smoothness of the data-fitting term leads to the difficulty in solving the optimization problem of GSRL, and available solvers usually suffer either slow convergence or restrictions on the dictionary. In this paper, we propose a class of efficient solvers for GSRL in a block coordinate descent manner, including group-wise cyclic minimization (GCM) for group-wise orthonormal dictionary and generalized GCM (G-GCM) for general dictionary. Both strict descent property and global convergence are proved. To cope with signal processing applications, the complex-valued multiple measurement vectors (MMV) case is considered. The proposed algorithm can also be used for the fast implementation of methods with theoretical equivalence to GSRL, e.g., GSPICE. Significant superiority in computational efficiency is verified by simulation results. [ABSTRACT FROM AUTHOR]