## Abstract

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.

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 language | English |
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Pages (from-to) | 1329-1350 |

Number of pages | 22 |

Journal | Discrete and Continuous Dynamical Systems - Series S |

Volume | 10 |

Issue number | 6 |

Early online date | 30 Jun 2017 |

DOIs | |

Publication status | Published - Dec 2017 |

## Keywords

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