Efficient Proximal Gradient Algorithms for Joint Graphical Lasso

We consider learning as an undirected graphical model from sparse data. While several efficient algorithms have been proposed for graphical lasso (GL), the alternating direction method of multipliers (ADMM) is the main approach taken concerning joint graphical lasso (JGL). We propose proximal gradient procedures with and without a backtracking option for the JGL. These procedures are first-order methods and relatively simple, and the subproblems are solved efficiently in closed form. We further show the boundedness for the solution of the JGL problem and the iterates in the algorithms. The numerical results indicate that the proposed algorithms can achieve high accuracy and precision, and their efficiency is competitive with state-of-the-art algorithms.

A new conjugate gradient algorithms using conjugacy condition for solving unconstrained optimization

The primarily objective of this paper which is indicated in the field of conjugate gradient algorithms for unconstrained optimization problems and algorithms is to show the advantage of the new proposed algorithm in comparison with the standard method which is denoted as. Hestenes Stiefel method, as we know the coefficient conjugate parameter is very crucial for this reason, we proposed a simple modification of the coefficient conjugate gradient which is used to derived the new formula for the conjugate gradient update parameter described in this paper. Our new modification is based on the conjugacy situation for nonlinear conjugate gradient methods which is given by the conjugacy condition for nonlinear conjugate gradient methods and added a nonnegative parameter to suggest the new extension of the method. Under mild Wolfe conditions, the global convergence theorem and lemmas are also defined and proved. The proposed method's efficiency is programming and demonstrated by the numerical instances, which were very encouraging.

A review of motion planning algorithms for intelligent robots

Principles of typical motion planning algorithms are investigated and analyzed in this paper. These algorithms include traditional planning algorithms, classical machine learning algorithms, optimal value reinforcement learning, and policy gradient reinforcement learning. Traditional planning algorithms investigated include graph search algorithms, sampling-based algorithms, interpolating curve algorithms, and reaction-based algorithms. Classical machine learning algorithms include multiclass support vector machine, long short-term memory, Monte-Carlo tree search and convolutional neural network. Optimal value reinforcement learning algorithms include Q learning, deep Q-learning network, double deep Q-learning network, dueling deep Q-learning network. Policy gradient algorithms include policy gradient method, actor-critic algorithm, asynchronous advantage actor-critic, advantage actor-critic, deterministic policy gradient, deep deterministic policy gradient, trust region policy optimization and proximal policy optimization. New general criteria are also introduced to evaluate the performance and application of motion planning algorithms by analytical comparisons. The convergence speed and stability of optimal value and policy gradient algorithms are specially analyzed. Future directions are presented analytically according to principles and analytical comparisons of motion planning algorithms. This paper provides researchers with a clear and comprehensive understanding about advantages, disadvantages, relationships, and future of motion planning algorithms in robots, and paves ways for better motion planning algorithms in academia, engineering, and manufacturing.

Proximal Algorithms for Discrete-Level Phase-Shifting Mask Design with Application to Optogenetics

This work studies the problem of designing computer-generated holograms using phase-shifting masks limited to represent only a small number of discrete phase levels. This problem has various applications, notably in the emerging field of optogenetics and lithography. A novel regularized cost function is proposed for the problem at hand that penalizes the unfeasible phase levels. Since the proposed cost function is non-smooth, we derive proper proximal gradient algorithms for its minimization. Simulation results, considering an optogenetics application, demonstrate that the proposed proximal gradient algorithm yields better performance as compared to other algorithms proposed in the literature.

CONTROL OF PASSAGE THROUGH RESONANCE ZONE FOR 1-ROTOR VIBRATION UNIT WITH TIME-VARYING LOAD

The speed-gradient algorithms for controlled passage through the resonance zone of the one-rotor vibration unit are studied by computer simulation. The objective of the study is to analyze dependence of the control performance on the loading mode and the electric drive dynamics. In order to obtain an algorithm better suitable for practical implementation the theoretically designed algorithm is simplified by simplifying the expression for the total energy. First of all, we neglect the terms corresponding to the kinetic and potential energy of the load, since there are no load mass sensors on the stand. the term containing the inclination angle of the platform is neglected. In addition, the platform inclination angle and dynamics of the drives were neglected too. Efficiency of the proposed simplified algorithm for different loading modes, including linear loading with different loading rates and sine-shaped oscillatory loading.