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On the relationship between bilevel decomposition algorithms and direct interior-point methods

Listed author(s):
  • Nogales Martín, Francisco Javier
  • Miguel, Angel Víctor de
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    Engineers have been using bilevel decomposition algorithms to solve certain nonconvex large-scale optimization problems arising in engineering design projects. These algorithms transform the large-scale problem into a bilevel program with one upperlevel problem (the master problem) and several lower-level problems (the subproblems). Unfortunately, there is analytical and numerical evidence that some of these commonly used bilevel decomposition algorithms may fail to converge even when the starting point is very close to the minimizer. In this paper, we establish a relationship between a particular bilevel decomposition algorithm, which only performs one iteration of an interior-point method when solving the subproblems, and a direct interior-point method, which solves the problem in its original (integrated) form. Using this relationship, we formally prove that the bilevel decomposition algorithm converges locally at a superlinear rate. The relevance of our analysis is that it bridges the gap between the incipient local convergence theory of bilevel decomposition algorithms and the mature theory of direct interior-point methods.

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    Paper provided by Universidad Carlos III de Madrid. Departamento de Estadística in its series DES - Working Papers. Statistics and Econometrics. WS with number ws042509.

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    Date of creation: Apr 2004
    Handle: RePEc:cte:wsrepe:ws042509
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    1. Blomvall, Jorgen & Lindberg, Per Olov, 2002. "A Riccati-based primal interior point solver for multistage stochastic programming," European Journal of Operational Research, Elsevier, vol. 143(2), pages 452-461, December.
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