Inverse truss design as a conic mathematical program with equilibrium constraints. (English) Zbl 1369.49032
Summary: 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.
MSC:
| 49K40 | Sensitivity, stability, well-posedness |
| 74P05 | Compliance or weight optimization in solid mechanics |
| 49M05 | Numerical methods based on necessary conditions |
| 90C30 | Nonlinear programming |
Keywords:
mathematical programs with equilibrium constraints; conic optimization; truss topology optimizationReferences:
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