Model order reduction with Galerkin projection applied to nonlinear optimization with infeasible primal‐dual interior point method

[1]  Jan Dirk Jansen,et al.  Accelerating iterative solution methods using reduced‐order models as solution predictors , 2006 .

[2]  Yuri V. Vassilevski,et al.  Choice of initial guess in iterative solution of series of systems arising in fluid flow simulations , 2006, J. Comput. Phys..

[3]  Jacob Fish,et al.  Multiple scale eigendeformation-based reduced order homogenization , 2009 .

[4]  Margaret H. Wright,et al.  Why a Pure Primal Newton Barrier Step May be Infeasible , 1995, SIAM J. Optim..

[5]  Damiano Pasetto,et al.  A reduced order model‐based preconditioner for the efficient solution of transient diffusion equations , 2017 .

[6]  C. Fleury,et al.  A family of MMA approximations for structural optimization , 2002 .

[7]  Christian Rey,et al.  Iterative accelerating algorithms with Krylov subspaces for the solution to large-scale nonlinear problems , 2004, Numerical Algorithms.

[8]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[9]  T. Tsuchiya,et al.  On the formulation and theory of the Newton interior-point method for nonlinear programming , 1996 .

[10]  P. Wriggers,et al.  An interior‐point algorithm for elastoplasticity , 2007 .

[11]  Krister Svanberg,et al.  A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations , 2002, SIAM J. Optim..

[12]  Charbel Farhat,et al.  A FETI‐preconditioned conjugate gradient method for large‐scale stochastic finite element problems , 2009 .

[13]  Radek Kucera,et al.  An interior-point algorithm for the minimization arising from 3D contact problems with friction , 2013, Optim. Methods Softw..

[14]  B. Haasdonk,et al.  A new local reduced basis discontinuous Galerkin approach for heterogeneous multiscale problems , 2011 .

[15]  Juan Du,et al.  Non-linear model reduction for the Navier-Stokes equations using residual DEIM method , 2014, J. Comput. Phys..

[16]  Emmanuel Roubin,et al.  Reduced order modeling strategies for computational multiscale fracture , 2017 .

[17]  K. Svanberg The method of moving asymptotes—a new method for structural optimization , 1987 .

[18]  A. Simone,et al.  POD-DEIM model order reduction for strain softening viscoplasticity , 2017 .

[19]  Charbel Farhat,et al.  Progressive construction of a parametric reduced‐order model for PDE‐constrained optimization , 2014, ArXiv.

[20]  Muruhan Rathinam,et al.  Dynamic Iteration Using Reduced Order Models: A Method for Simulation of Large Scale Modular Systems , 2002, SIAM J. Numer. Anal..

[21]  Knut-Andreas Lie,et al.  The localized reduced basis multiscale method for two‐phase flows in porous media , 2014, 1405.2810.

[22]  K. Anstreicher,et al.  On the convergence of an infeasible primal-dual interior-point method for convex programming , 1994 .

[23]  Jorge Nocedal,et al.  A trust region method based on interior point techniques for nonlinear programming , 2000, Math. Program..

[24]  Jorge Nocedal,et al.  An Interior Point Algorithm for Large-Scale Nonlinear Programming , 1999, SIAM J. Optim..

[25]  P. Wriggers,et al.  An adaptive model order reduction with Quasi‐Newton method for nonlinear dynamical problems , 2016 .

[26]  J. Herskovits Feasible Direction Interior-Point Technique for Nonlinear Optimization , 1998 .

[27]  Bert Pluymers,et al.  Adaptive model reduction technique for large-scale dynamical systems with frequency-dependent damping , 2018 .

[28]  Edmond Chow,et al.  Updating incomplete factorization preconditioners for model order reduction , 2016, Numerical Algorithms.

[29]  P Kerfriden,et al.  Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems. , 2011, Computer methods in applied mechanics and engineering.

[30]  Peter Wriggers,et al.  An adaptive model order reduction by proper snapshot selection for nonlinear dynamical problems , 2016 .