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Sufficient Optimality Conditions in Bilevel Programming

Author

Listed:
  • Patrick Mehlitz

    (Institute of Mathematics, Brandenburgische Technische Universität Cottbus–Senftenberg, 03046 Cottbus, Germany)

  • Alain B. Zemkoho

    (School of Mathematics, University of Southampton, Southampton SO17 1BJ, United Kingdom)

Abstract

This paper is concerned with the derivation of first- and second-order sufficient optimality conditions for optimistic bilevel optimization problems involving smooth functions. First-order sufficient optimality conditions are obtained by estimating the tangent cone to the feasible set of the bilevel program in terms of initial problem data. This is done by exploiting several different reformulations of the hierarchical model as a single-level problem. To obtain second-order sufficient optimality conditions, we exploit the so-called value function reformulation of the bilevel optimization problem, which is then tackled with the aid of second-order directional derivatives. The resulting conditions can be stated in terms of initial problem data in several interesting situations comprising the settings where the lower level is linear or possesses strongly stable solutions.

Suggested Citation

  • Patrick Mehlitz & Alain B. Zemkoho, 2021. "Sufficient Optimality Conditions in Bilevel Programming," Mathematics of Operations Research, INFORMS, vol. 46(4), pages 1573-1598, November.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:4:p:1573-1598
    DOI: 10.1287/moor.2021.1122
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