Inverse truss design as a conic mathematical program with equilibrium constraints

Michal Kocvara, JV Outrata

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We formulate an inverse optimal design problem as a Mathematical Programming
problem with Equilibrium Constraints (MPEC). The equilibrium constraints are in
the form of a second-order conic optimization problem. Using the so-called
Implicit Programming technique, we reformulate the bilevel optimization problem
as a single-level nonsmooth nonconvex problem. The major part of the article is
devoted to the computation of a subgradient of the resulting composite
objective function. The article is concluded by numerical examples
demonstrating, for the first time, that the Implicit Programming technique can be efficiently used in the numerical solution of MPECs with conic constraints on the lower level.
Original languageEnglish
Pages (from-to)1329-1350
Number of pages22
JournalDiscrete and Continuous Dynamical Systems - Series S
Issue number6
Early online date30 Jun 2017
Publication statusPublished - Dec 2017


  • Mathematical programs with equilibrium constraints
  • conic optimization
  • truss topology optimization


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