Sufficient Optimality Conditions in Bilevel Programming

Patrick Mehlitz () and Alain B. Zemkoho ()
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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

Mathematics of Operations Research, 2021, vol. 46, issue 4, 1573-1598

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.

Keywords: Primary: 90C30; 90C33; 90C46; secondary: 49J52; 49J53; Primary: nonlinear programming; optimality conditions; secondary: complementarity programming; nondifferentiable programming; parametric programming; bilevel optimization; first-order sufficient optimality conditions; second-order directional derivatives; second-order sufficient optimality conditions (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:46:y:2021:i:4:p:1573-1598

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