References
- Allaire , G. 2002 . Shape Optimization by the Homogenization Method , Berlin, Heidelberg, New York : Springer .
- Antil , H. , Hoppe , R. H.W. and Linsenmann , Chr. 2007 . Path-following primal-dual interior-point methods for shape optimization . J. Numer. Math. , 15 ( 2 ) : 81 – 100 .
- Bakhvalov , N. and Panasenko , G. 1984 . Averaging Processes in Periodic Media , Moscow : Nauka .
- Bendsœ , M. P. 1995 . Optimization of Structural Topology, Shape, and Material , Berlin : Springer .
- Bensoussan , A. , Lions , J. L. and Papanicolaou , G. 1978 . Asymptotic Analysis for Periodic Structures , North-Holland, Amsterdam : Elsevier Science Publishers .
- Byrd , R. H. , Hribar , M. E. and Nocedal , J. 1999 . An interior point algorithm for large scale nonlinear programming . SIAM J. Optim. , 9 ( 4 ) : 877 – 900 .
- Delfour , M. C. and Zolesio , J. P. 2001 . Shapes and Geometries: Analysis, Differential Calculus, and Optimization , Philadelphia : SIAM .
- Deuflhard , P. 2004 . Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms , Berlin, Heidelberg, New York : Springer .
- El-Bakry , A. , Tapia , R. , Tsuchiya , T. and Zhang , Y. 1996 . On the formulation and theory of the Newton interior-point method for nonlinear programming . J. Optim. Theory Appl. , 89 : 507 – 541 .
- Fiacco , A. V. and McCormick , G. P. 1968 . Nonlinear Programming. Sequential Unconstrained Minimization Techniques , New York : John Wiley and Sons . Republished by SIAM, Philadelphia, Pennsylvania, 1990
- Forsgren , A. , Gill , P. E. and Wright , M. H. 2002 . Interior methods for nonlinear optimization . SIAM Review , 44 : 525 – 597 .
- den Hertog , D. 1994 . Interior Point Approach to Linear, Quadratic and Convex Programming , Dordrecht : Kluwer .
- Hoppe , R. H.W. and Petrova , S. I. 2004 . Optimal shape design in biomimetics based on homogenization and adaptivity . Math. Comput. Simul. , 65 : 257 – 272 .
- Hoppe , R. H.W. and Petrova , S. I. 2004 . Primal-dual Newton interior point methods in shape and topology optimization . Numer. Linear Algebra Appl. , 11 ( 5-6 ) : 413 – 429 .
- Hoppe , R. H.W. and Petrova , S. I. 2006 . Shape optimization of biomorphic ceramics with microstructures by homogenization modeling , Edited by: Mielke , A. 395 – 424 . Berlin, Heidelberg, New York : Springer .
- Hoppe , R. H.W. , Kladny , R. , Petrova , S. I. and Sieber , H. Functional Micro-and Nanosystems, Proceedings of the 4th Caesarium . June 16–18 2003 , Bonn. Modeling, simulation, and optimization of microstructured biomorphic materials , Edited by: Hoffmann , K.H. pp. 35 – 54 . Berlin, Heidelberg, New York : Springer .
- Jikov , V. V. , Kozlov , S. M. and Oleinik , O. A. 1994 . Homogenization of Differential Operators and Integral Functionals , Springer .
- Mohammadi , B. and Pironneau , O. 2001 . Applied Shape Optimization for Fluids , Oxford : Oxford University Press .
- Nocedal , J. and Wright , S. 1999 . Numerical Optimization , New York : Springer .
- Pankov , A. 1997 . G-convergence and Homogenization of Nonlinear Partial Differential Operators , Dordrecht : Kluwer .
- Sokolowski , J. and Zol\'esio , J.-P. 1992 . Introduction to Shape Optimization , Springer . Springer Series in Computational Mathematics 16
- Wittum , G. 1989 . On the convergence of multigrid methods with transforming smoothers. Theory with applications to the Navier--Stokes equations . Numer. Math. , 57 : 15 – 38 .
- Wright , M. H. 1992 . Interior methods for constrained optimization . Acta Numerica , 1 : 341 – 407 .
- Zienkiewicz , O. C. and Zhu , J. Z. 1987 . A simple error estimator and adaptive procedure for practical engineering analysis . Intern. J. Numer. Methods Eng. , 24 : 337 – 357 .