We investigate reduced-space Newton-Krylov (NK) algorithms for engineering parameter optimization problems constrained by partial-differential equations. We review reduced-space and full-space optimization algorithms, and we show that the efficiency of the reduced-space strategy can be improved significantly with inexact-Hessianvector products computed using approximate second-order adjoints. R...

Optimization problems constrained by nonlinear partial differential equations have been the focus of intense research in scientific computing lately. Current methods for the parallel numerical solution of such problems involve sequential quadratic programming (SQP), with either reduced or full space approaches. In this paper we propose and investigate a class of parallel full space SQP Lagrange...

Corrections are computed to the classical static isotropic solution of general relativity, arising from nonperturbative quantum gravity effects. A slow rise of the effective gravitational coupling with distance is shown to involve a genuinely nonperturbative scale, closely connected with the gravitational vacuum condensate, and thereby related to the observed effective cosmological constant. We...

We show that a lithium experiment has a potential to confirm or reject the value 1.5% of the solar luminosity attributed to a CNO-cycle by the standard solar model and to prove that the difference between total energy release of the Sun and what is produced in a hydrogen sequence is really produced in CNO cycle. This will be the stringent test of the theory of stellar evolution and the terminat...

Nonlinear multigrid methods such as the Full Approximation Scheme (FAS) and Newton-multigrid (Newton-MG) are well established as fast solvers for nonlinear PDEs of elliptic and parabolic type. In this paper we consider Newton-MG and FAS iterations applied to second order differential operators with nonlinear diffusion coefficient. Under mild assumptions arising in practical applications, an app...

In solving stiff systems of ordinary differential equations using BDF methods, Jacobians needed for quasi-Newton iteration are frequently computed using finite differences. Round-off errors in the finite-difference approximation can lead to Newton failures forcing the code to choose its time steps based on “stability” rather than accuracy considerations. When standard stepsize control is used, ...

Recently, we have extended SDP by adding a quadratic term in the objective function and give a potential reduction algorithm using NT directions. This paper presents a predictor-corrector algorithm using both Dikin-type and Newton centering steps and studies properties of Dikin-type step. In this algorithm, when the condition K(XS) is less than a given number K0, we use Dikin-type step. Otherwi...

A dual logarithmic barrier method for solving large, sparse semidefinite programs is proposed in this paper. The method avoids any explicit use of the primal variable X and therefore is well-suited to problems with a sparse dual matrix S. It relies on inexact Newton steps in dual space which are computed by the conjugate gradient method applied to the Schur complement of the reduced KKT system....

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 new class of rigorous methods for derivative-free optimization with the aim delivering efficient and robust numerical performance functions all types, from smooth to non-smooth, under different noise regimes. To this end, we have developed methods, called Full-Low Evaluation organized around two main types iterations. The first iteration type (called Full-Eval) is expensive in func...