Abstract Optimization problems that include regularization functions in their objectives are regularly solved many applications. When one seeks second-order methods for such problems, it may be desirable to exploit specific properties of some these when accounting curvature information the solution steps speed up convergence. In this paper, we propose SCORE (self-concordant regularization) fram...

The objectives of this study were to provide new parameters to better understand labor curves, and to provide a model to predict the time to full cervical dilation (CD). We studied labor curves using the retrospective records of 594 nulliparas, including at term, spontaneous labor onset, and singleton vertex deliveries of normal birth weight infants. We redefined the parameters of Friedman's la...

Newton’s method is a classical method for solving a nonlinear equation F (z) = 0. We derive inexact Newton steps that lead to an inexact Newton method, applicable near a solution. The method is based on solving for a particular F (zk′) during p consecutive iterations k = k′, k′ + 1, . . . , k′ + p − 1. One such p-cycle requires 2 − 1 solves with the matrix F (zk′). If matrix factorization is us...

where F (ξ) is a nonlinear operator from a real Euclidean space of dimension n or Hilbert space into itself. The Euclidean norm and corresponding inner product will be denoted by ‖·‖1 and (·, ·)1 respectively. A general different inner product with a weight function and the corresponding norm will be denoted by (·, ·)0 and ‖ · ‖ respectively. In the first part of this article (Sects. 2 and 3) w...

The adjoint Newton algorithm (ANA) is based on the firstand second-order adjoint techniques allowing one to obtain the ‘‘Newton line search direction’’ by integrating a ‘‘tangent linear model’’ backward in time (with negative time steps). Moreover, the ANA provides a new technique to find Newton line search direction without using gradient information. The error present in approximating the Hes...

We discuss the solution of numerically ill-posed overdetermined systems of equations using Tikhonov a-priori-based regularization. When the noise distribution on the measured data is available to appropriately weight the fidelity term, and the regularization is assumed to be weighted by inverse covariance information on the model parameters, the underlying cost functional becomes a random varia...

The purpose of this work was to investigate the utility of implicit integration methods for molecular dynamics (MD) simulation. Implicit methods were investigated in an attempt to address the bottleneck associated with short, stability-limited step size lengths available to the explicit methods currently in widespread use. Two implicit methods were compared to the current standard for time inte...

In this work, we present a two-dimensional mixed-hybrid finite element model of variably saturated flow on unstructured triangular meshes. Velocities are approximated using lowest order Raviart-Thomas (RT0) elements with piecewise constant pressure. The resulting nonlinear systems of algebraic equations are solved using Picard or Newton iterations in combination with ad hoc preconditioning tech...

This paper applies genetic algorithms to the problem of induction motor parameter determination. Generally available manufacturers published data like starting torque, breakdown torque, full load torque, full load power factor etc, are used to determine the motor parameters for subsequent use in studying machine transients. Results from several versions of the genetic algorithm are presented as...

In this paper, we present SILCA-Newton-Krylov, a new method for accurate, efficient and robust timedomain VLSI circuit simulation. Similar to SPICE, SILCA-Newton-Krylov uses time-difference and Newton-Raphson for solving nonlinear differential equations from circuit simulation. But different from SPICE, SILCA-Newton-Krylov explores a preconditioned flexible generalized minimal residual (FGMRES)...