CONLIN: An efficient dual optimizer based on convex approximation concepts. The Convex Linearization method (CONLIN) exhibits many interesting features and it is applicable to a broad class of structural optimization problems. The method employs mixed design variables (either direct or reciprocal) in order to get first order, conservative approximations to the objective function and to the constraints. The primary optimization problem is therefore replaced with a sequence of explicit approximate problems having a simple algebraic structure. The explicit subproblems are convex and separable, and they can be solved efficiently by using a dual method approach. In this paper, a special purpose dual optimizer is proposed to solve the explicit subproblem generated by the CONLIN strategy. The maximum of the dual function is sought in a sequence of dual subspaces of variable dimensionality. The primary dual problem is itself replaced with a sequence of approximate quadratic subproblems with non-negativity constraints on the dual variables. Because each quadratic subproblem is restricted to the current subspace of non zero dual variables, its dimensionality is usually reasonably small. Clearly, the Hessian matrix does not need to be inverted (it can in fact be singular), and no line search process is necessary. An important advantage of the proposed maximization method lies in the fact that most of the computational effort in the iterative process is performed with reduced sets of primal variables and dual variables. Furthermore, an appropriate active set strategy has been devised, that yields a highly reliable dual optimizer.

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  1. Facchinei, Francisco; Lampariello, Lorenzo; Scutari, Gesualdo: Feasible methods for nonconvex nonsmooth problems with applications in green communications (2017)
  2. Munro, Dirk; Groenwold, Albert A.: On sequential approximate simultaneous analysis and design in classical topology optimization (2017)
  3. Ribeiro, Ademir A.; Sachine, Mael; Santos, Sandra A.: On the augmented subproblems within sequential methods for nonlinear programming (2017)
  4. Nagy, Attila P.; IJsselmuiden, Samuel T.; Abdalla, Mostafa M.: Isogeometric design of anisotropic shells: optimal form and material distribution (2013)
  5. Bruggi, Matteo; Duysinx, Pierre: Topology optimization for minimum weight with compliance and stress constraints (2012)
  6. Hassani, Behrooz; Khanzadi, Mostafa; Tavakkoli, S.Mehdi: An isogeometrical approach to structural topology optimization by optimality criteria (2012)
  7. Polynkin, Andrey; Toropov, Vassili V.: Mid-range metamodel assembly building based on linear regression for large scale optimization problems (2012)
  8. Tavakoli, Rouhollah; Zhang, Hongchao: A nonmonotone spectral projected gradient method for large-scale topology optimization problems (2012)
  9. Brüls, Olivier; Lemaire, Etienne; Duysinx, Pierre; Eberhard, Peter: Optimization of multibody systems and their structural components (2011)
  10. Silva, Mariana; Tortorelli, Daniel A.; Norato, Julian A.; Ha, Christopher; Bae, Ha-Rok: Component and system reliability-based topology optimization using a single-loop method (2010)
  11. Yang, Dixiong; Yang, Pixin: Numerical instabilities and convergence control for convex approximation methods (2010)
  12. Magnusson, Johan; Klarbring, Anders; Sethson, Magnus: Design and configuration of neuro mechanical networks (2009)
  13. Rozvany, George I.N.: A critical review of established methods of structural topology optimization (2009)
  14. Stingl, M.; Kočvara; Leugering, G.: A new non-linear semidefinite programming algorithm with an application to multidisciplinary free material optimization (2009)
  15. Stingl, M.; Kočvara, M.; Leugering, G.: A sequential convex semidefinite programming algorithm with an application to multiple-load free material optimization (2009)
  16. Wadbro, Eddie; Berggren, Martin: Megapixel topology optimization on a graphics processing unit (2009)
  17. Lemaire, E.; Rochus, V.; Golinval, J.-C.; Duysinx, P.: Microbeam pull-in voltage topology optimization including material deposition constraint (2008)
  18. Luo, Zhen; Tong, Liyong; Wang, Michael Yu; Wang, Shengyin: Shape and topology optimization of compliant mechanisms using a parameterization level set method (2007)
  19. Svanberg, Krister; Werme, Mats: Sequential integer programming methods for stress constrained topology optimization (2007)
  20. Ponthot, J.-P.; Kleinermann, J.-P.: A cascade optimization methodology for automatic parameter identification and shape/process optimization in metal forming simulation (2006)

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