A nonlinear elimination preconditioned inexact Newton (NEPIN) algorithm is proposed for problems with localized strong nonlinearities. Due to unbalanced nonlinearities (``nonlinear stiffness''), the traditional method often exhibits a long plateau in norm of residual or even fails converge. NEPIN implicitly removes components causing trouble global convergence through correction based on within...

For unconstrained optimization, an inexact Newton algorithm is proposed recently, in which the preconditioned conjugate gradient method is applied to solve the Newton equations. In this paper, we improve this algorithm by efficiently using automatic differentiation and establish a new inexact Newton algorithm. Based on the efficiency coefficient defined by Brent, a theoretical efficiency ratio ...

An algorithm for finding sums of hermitian squares decompositions for polynomials in noncommuting variables is presented. The algorithm is based on the “Newton chip method”, a noncommutative analog of the classical Newton polytope method, and semidefinite programming.

In this paper, a novel algorithm for the load flow analysis problem in an islanded microgrid is proposed. The problem is modeled without any slack bus by considering the steady state frequency as one of the load flow variables. To model different control modes of DGs, such as droop, PV and PQ, in an islanded microgrid, a new formula for load flow equations is proposed. A hybrid optimization alg...

By a modification of the classic-Newton direction in scaled version for linear optimization, we give a new interior-point algorithm based on a very simple function. The algorithm uses full modified-Newton step, thus no need to perform line search. In the processing of the algorithm, the simple function is used to control the searching direction and measure the proximity of iterates to the centr...

The full-space Lagrange–Newton algorithm is one of the numerical algorithms for solving problems arising from optimization problems constrained by nonlinear partial differential equations. Newton-type methods enjoy fast convergence when the nonlinearity in the system is well-balanced; however, for some problems, such as the control of incompressible flows, even linear convergence is difficult t...

We propose a Newton-CG primal proximal point algorithm for solving large scale log-determinant optimization problems. Our algorithm employs the essential ideas of the proximal point algorithm, the Newton method and the preconditioned conjugate gradient solver. When applying the Newton method to solve the inner sub-problem, we find that the log-determinant term plays the role of a smoothing term...