The Worst-Case Multiple Load FMO Problem Revisited

  • Michal Kočcvara
  • Michael Stingl
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 137)


We propose a new formulation of the worst-case multiple-load problem of free material optimization. It leads to an optimization problem with bilinear matrix inequality constraints. The resulting problem can be solved by a recently developed code PENBMI. The new formulation is shown to be more computationally efficient than the recently used one.


Free material optimization semidefinite programming 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ben-Tal, A., Kočvara, M., Nemirovski, A., and Zowe, J. (1997). Free material design via semidefinite programming. The multi-load case with contact conditions. SIAM J. Optimization, 9:813–832.CrossRefGoogle Scholar
  2. Bendsøe, M. and Sigmund, O. (2002). Topology Optimization. Theory, Methods and Applications. Springer-Verlag, Heidelberg.zbMATHGoogle Scholar
  3. Bendsøe, M. P., Guades, J. M., Haber, R., Pedersen, P., and Taylor, J. E. (1994). An analytical model to predict optimal material properties in the context of optimal structural design. J. Applied Mechanics, 61:930–937.zbMATHGoogle Scholar
  4. Hörnlein, H., Kočvara, M., and Werner, R. (2001). Material optimization: Bridging the gap between conceptual and preliminary design. Aerospace Science and Technology, 5:541–554.zbMATHCrossRefGoogle Scholar
  5. Kočvara, M., Zibulevsky, M., and Zowe, J. (1998). Mechanical design problems with unilateral contact. M2AN Mathematical Modelling and Numerical Analysis, 32:255–282.Google Scholar
  6. Kočvara, M., Leibfritz, F., Stingl, M., and Henrion, D. (2004). A nonlinear SDP algorithm for static output feedback problems in COMPlib. LAAS-CNRS research report no. 04508, LAAS, Toulouse.Google Scholar
  7. Kočcvara, M. and Stingl, M. (2003). PENNON—a code for convex nonlinear and semidefinite programming. Optimization Methods and Software, 18(3):317–333.MathSciNetCrossRefGoogle Scholar
  8. Werner, R. (2000). Free Material Optimization. Mathematical Analysis and Numerical Solution. PhD thesis, Inst. of Applied Mathematics, University of Erlangen.Google Scholar
  9. Zowe, J., Kočvara, M., and Bendsøe, M. (1997). Free material optimization via mathematical programming. Mathematical Programming, Series B, 79:445–466.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Michal Kočcvara
    • 1
    • 2
  • Michael Stingl
    • 3
  1. 1.Institute of Information Theory and AutomationAcademy of Sciences of the Czech RepublicPrague
  2. 2.Faculty of Electrical EngineeringCzech Technical UniversityPragueCzech Republic
  3. 3.Institute of Applied MathematicsUniversity of ErlangenErlangenGermany

Personalised recommendations