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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-9740908b-be19-4d67-91d3-8fa4c2c607ba

Czasopismo

Control and Cybernetics

Tytuł artykułu

Dynamic programming approach to shape optimization

Autorzy Fulmański, P.  Nowakowski, A. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
Abstrakty
EN We provide a dynamic programming approach through the level set setting to structural optimization problems. By constructing a dual dynamic programming method we provide the verification theorem for optimal and "−optimal solutions of shape optimization problem.
Słowa kluczowe
EN dynamic programming   shape optimization  
Wydawca Systems Research Institute, Polish Academy of Sciences
Czasopismo Control and Cybernetics
Rocznik 2014
Tom Vol. 43, no. 3
Strony 379--401
Opis fizyczny Bibliogr. 27 poz.
Twórcy
autor Fulmański, P.
autor Nowakowski, A.
Bibliografia
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6. FULMAŃSKI, P., LAURIN, A., SCHEID, J.F. and SOKOŁOWSKI, J. (2007) A Level Set Method in Shape and Topology Optimization for Variational Inequalities. International Journal of Applied Mathematics and Computer Science, 17, 413-430.
7. GALEWSKA, E. and NOWAKOWSKI, A. (2006) A dual dynamic programming for multidimensional elliptic optimal control problems. Numer. Funct. Anal. Optim., 27, 279–289.
8. GARREAU, S., GUILLAUME, P. and MASMOUDI, M. (2001) The topological Asymptotic for PDE Systems: the Elasticity Case. SIAM Journal on Control Optimization, 39, 1756–1778.
9. HASLINGER, J. and MÄKINEN, R. (2003) Introduction to Shape Optimization. Theory, Approximation and Computation. SIAM Publications, Philadelphia.
10. HÜBER, S., STADLER, G. and WOHLMUTH, B. (2008) A Primal-Dual Active Set Algorithm for Three Dimensional Contact Problems with Coulomb Friction. SIAM J. Sci. Comput, 30 (2), 572-596.
11. MAURER, H., OBERLE, J. (2002) Second order sufficient conditions for optimal control problems with free final time: the Riccati approach. SIAM J. Control Optim, 41 (2) 380-403.
12. MYŚLIŃSKI, A. (2004) A Level Set Method for Shape Optimization of Contact Problems. In: P. Neittaanmäki ed. CD-ROM Proceedings of European Congress on Computational Methods in Applied Sciences and Engineering, Jyväskylä, Finland, 24-28 July 2004. WIT Press, Southampton–Boston.
13. MYŚLIŃSKI, A. (2005) Topology and Shape Optimization of Contact Problems using a Level Set Method. In: J. Herskovits, S. Mazorche, A. Canelas, eds., Proceedings of VI World Congresses of Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil, 30 May - 2 June 2005. CD-ROM: WCSMO6, International Society for Structural and Multidisciplinary Optimization.
14. MYŚLIŃSKI, A. (2010) Radial Basis Function Level Set Method for Structural Optimization. Control Cybernet. 39, 3, 627–645.
15. NOWAKOWSKI, A. (2008) " -Value Function and Dynamic Programming. Journal of Optimization Theory and Applications, 138, 1, 85–93.
16. NOWAKOWSKI, A. (1992) The dual dynamic programming. Proceedings of the American Mathematical Society, 116, 1089–1096.
17. NOWAKOWSKI, A. (2013) "–optimal value and approximate multidimensional dual dynamic programming. Asian J. Control 15, 2, 444–452.
18. NOWAKOWSKI, A. and SOKOŁOWSKI J. (2012) On dual dynamic programming in shape control. Commun. Pure Appl. Anal. 11, 6, 2473–2485.
19. SETHIAN, J. A. (1987) Numerical Methods for Propagating Fronts. In: P. Concus and R, Finn, eds., Variational Methods for Free Surface Interfaces. Springer–Verlag.
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21. SETHIAN, J. A. and A. WIEGMANN (2000) Structural Boundary Design via Level Set and Immersed Interface Methods. Journal of Computational Physics 163, 489–528.
22. SOKOŁOWSKI, J. and ZOLESIO, J.P. (1992) Introduction to Shape Optimization. Springer–Verlag.
23. SOKOLOWSKI, J. and ZOCHOWSKI, A. (1999) Topological derivative for elliptic problems. Inverse Problems, 15, 123–134.
24. SOKOŁOWSKI, J. and ŻOCHOWSKI, A. (2003) Optimality Conditions for Simultaneous Topology and Shape Optimization. SIAM Journal of Control, 42 (4), 1198–1221.
25. SOKOŁOWSKI, J. and ŻOCHOWSKI, A. (2004) On Topological Derivative in Shape Optimization. In: T. Lewiński, O. Sigmund, J. Sokołowski, A. Żochowski, eds., Optimal Shape Design and Modelling. Academic Printing House EXIT, Warsaw, Poland, 55–143.
26. SOKOŁOWSKI, J. and ŻOCHOWSKI, A. (2005) A Modeling of Topological Derivatives for Contact Problems. Numerische Mathematik 102 (1), 145– 179.
27. STADLER, G. (2004) Semismooth Newton and Augmented Lagrangian methods for a Simplified Friction Problem. SIAM Journal on Optimization 15 (1), 39–62.
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