The sparse nonlinear programming (SNP) problem has wide applications in signal and image processing, machine learning finance, etc. However, the computational challenge posed by SNP not yet been well resolved due to nonconvex discontinuous $$\ell _0$$ -norm involved. In this paper, we resolve numerical developing a fast Newton-type algorithm. As theoretical cornerstone, establish first-order op...

We propose a continuous-time second-order optimization algorithm for solving unconstrained convex problems with bounded Hessian. show that this alternative has comparable convergence rate to of the Newton–Raphson method, however structurally, it is amenable more efficient distributed implementation. present implementation our proposed and prove its via Lyapunov analysis. A numerical example dem...

For numerical optimization of the cost function of the maximum likelihood (ML) algorithm for angle-of-arrival (AOA) estimation, Newton-type method has been widely employed. In this paper, we apply the Newton-type method to the optimization of cost function for spectrum estimation-based AOA estimation algorithm of the conventional beamforming, the Capon beamfomring and the MUSIC algorithm. Expli...

introduction we aimed to introduce a 6-universal-prismatic-spherical (ups) parallel mechanism for the human jaw motion and theoretically evaluate its kinematic problem. we proposed a strategy to provide a fast and accurate solution to the kinematic problem. the proposed strategy could accelerate the process of solution-finding for the direct kinematic problem by reducing the number of required ...

The finite element setting for nonlinear elliptic PDEs directly leads to the minimization of convex functionals. Uniform ellipticity of the underlying PDE shows up as strict convexity of the arising nonlinear functional. The paper analyzes computational variants of Newton’s method for convex optimization in an affine conjugate setting, which reflects the appropriate affine transformation behavi...

We describe an algorithm for the numerical solution of a phase-field model (PFM) of microstructure evolution in polycrystalline materials. The PFM system of equations includes a local order parameter, a quaternion representation of local orientation and a species composition parameter. The algorithm is based on the implicit integration of a semidiscretization of the PFM system using a backward ...

A polynomial-based division algorithm and a corresponding hardware structure are proposed. The proposed algorithm is shown to be competitive to other conventional algorithms like the Newton-Raphson algorithm for up to about 32 bits accuracy. For example, using Newton-Raphson with less than 12 bits accuracy of the initial approximation, requires 33% more general multiplications than the proposed...