Full Newton nonlinear iteration is compared to use of a defect correction approach rst order Jacobian second order residual for solving the steady state compressible ow equations The Jacobian is constructed numerically and solved using a PCG type method with block ILU k preconditioning Numerical tests are carried out using the NACA airfoil at various free stream Mach numbers and Reynolds number...

‎a full nesterov-todd (nt) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using euclidean jordan algebra‎. ‎two types of‎ ‎full nt-steps are used‎, ‎feasibility steps and centering steps‎. ‎the‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...

We develop certified tracking procedures for Newton homotopies, which are homotopies for which only the constant terms are changed. For these homotopies, our certified procedures include using a constant predictor with Newton corrections, an Euler predictor with no corrections, and an Euler predictor with Newton corrections. In each case, the predictor is guaranteed to produce a point in the qu...

In [4] the second author presented a new primal-dual infeasible interior-point algorithm that uses full-Newton steps and whose iteration bound coincides with the best known bound for infeasible interior-point algorithms. Each iteration consists of a step that restores the feasibility for an intermediate problem (the so-called feasibility step) and a few (usual) centering steps. No more than O(n...

We show how the method of pseudo-transient continuation can be applied to improve the robustness of the Newton iteration within a nonlinear transient elasticity simulation. Pseudotransient continuation improves efficiency and robustness of the transient analysis by enabling larger time steps than possible with a Newton iteration. We illustrate the algorithm by reporting on a simulation of a buc...

In this paper we present a hybrid path-following algorithm that generates inexact Newton steps suited for solving large scale and/or degenerate nonlinear programs. The algorithm uses as a central region a relaxed notion of the central path, called quasicentral path, a generalized augmented Lagrangian function, weighted proximity measures, and a linesearch within a trust region strategy. We appl...

Recent efforts in differentiable non-linear programming have been focused on interior point methods, akin to penalty and barrier algorithms. In this paper, we address the classical equality constrained program solved using the simple quadratic loss penalty function/algorithm. The suggestion to use extrapolations to track the differentiable trajectory associated with penalized subproblems goes b...

the pseudo-elastic behavior of shape memory alloy (sma) truss and cantilever beam are investigated. brinson’s one-dimensional material model, which uses the twinned and detwinned martensite fractions separately as internal variables, is applied in the algorithm to establish the sma stress-strain characteristics. this material model also incorporates different young’s modulus for austenitic and ...

Getting a perfectly centered initial point for feasible path-following interior-point algorithms is hard practical task. Therefore, it worth to analyze other cases when the starting not necessarily centered. In this paper, we propose short-step weighted-path following algorithm (IPA) solving convex quadratic optimization (CQO). The latter based on modified search direction which obtained by tec...