Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2014 | 43 | nr 3 | 379--401
Tytuł artykułu

Dynamic Programming Aapproach to Shape Optimization

Treść / Zawartość
Warianty tytułu
Języki publikacji
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 ε-optimal solutions of shape optimization problem. (original abstract)
Opis fizyczny
  • University of Lodz
  • University of Lodz
  • BEDNARCZUK, E., PIERRE, M., ROUY, E. and SOKOŁOWSKI, J. (2000) Tangent sets in some functional spaces. Nonlinear Anal., 42, Ser. A: Theory Methods, 871-886.
  • BELLMAN, R. (1957) Dynamic Programming. Princeton University Press, Princeton.
  • BURGER, M., HACKL, B. and RING, W. (2004) Incorporating Topological Derivatives into Level Set Methods. Journal of Computational Physics 194 (1), 344-362.
  • DELFOUR,M. C. and ZOLESIO, J. P. (2001) Shapes and Geometries - Analysis, Differential Calculus and Optimization. Advances in Design and Control, SIAM.
  • FLEMING, W.H. and RISHEL, R.W. (1975) Deterministic and Stochastic Optimal Control. Springer Verlag, New York.
  • 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.
  • GALEWSKA, E. and NOWAKOWSKI, A. (2006) A dual dynamic programming for multidimensional elliptic optimal control problems. Numer. Funct. Anal. Optim., 27, 279-289.
  • 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.
  • HASLINGER, J. and MÄKINEN, R. (2003) Introduction to Shape Optimization. Theory, Approximation and Computation. SIAM Publications, Philadelphia.
  • 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.
  • 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.
  • 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.
  • 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.
  • MYŚLIŃSKI, A. (2010) Radial Basis Function Level Set Method for Structural Optimization. Control Cybernet. 39, 3, 627-645.
  • NOWAKOWSKI, A. (2008) " -Value Function and Dynamic Programming. Journal of Optimization Theory and Applications, 138, 1, 85-93.
  • NOWAKOWSKI, A. (1992) The dual dynamic programming. Proceedings of the American Mathematical Society, 116, 1089-1096.
  • NOWAKOWSKI, A. (2013) "-optimal value and approximate multidimensional dual dynamic programming. Asian J. Control 15, 2, 444-452.
  • NOWAKOWSKI, A. and SOKOŁOWSKI J. (2012) On dual dynamic programming in shape control. Commun. Pure Appl. Anal. 11, 6, 2473-2485.
  • SETHIAN, J. A. (1987) Numerical Methods for Propagating Fronts. In: P. Concus and R, Finn, eds., Variational Methods for Free Surface Interfaces. Springer-Verlag.
  • SETHIAN, J. A. (1996) A fast marching level set method for monotonically advancing fronts. Proc. Nat. Acad. Sci. 93 (4), 1591.
  • SETHIAN, J. A. and A. WIEGMANN (2000) Structural Boundary Design via Level Set and Immersed Interface Methods. Journal of Computational Physics 163, 489-528.
  • SOKOŁOWSKI, J. and ZOLESIO, J.P. (1992) Introduction to Shape Optimization. Springer-Verlag.
  • SOKOLOWSKI, J. and ZOCHOWSKI, A. (1999) Topological derivative for elliptic problems. Inverse Problems, 15, 123-134.
  • SOKOŁOWSKI, J. and ŻOCHOWSKI, A. (2003) Optimality Conditions for Simultaneous Topology and Shape Optimization. SIAM Journal of Control, 42 (4), 1198-1221.
  • 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.
  • SOKOŁOWSKI, J. and ŻOCHOWSKI, A. (2005) A Modeling of Topological Derivatives for Contact Problems. Numerische Mathematik 102 (1), 145- 179.
  • STADLER, G. (2004) Semismooth Newton and Augmented Lagrangian methods for a Simplified Friction Problem. SIAM Journal on Optimization 15 (1), 39-62.
Typ dokumentu
Identyfikator YADDA

Zgłoszenie zostało wysłane

Zgłoszenie zostało wysłane

Musisz być zalogowany aby pisać komentarze.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.