On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints

Holger Heitsch, René Henrion, Thomas Kleinert () and Martin Schmidt ()
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Holger Heitsch: Weierstrass Institute for Applied Analysis and Stochastics
René Henrion: Weierstrass Institute for Applied Analysis and Stochastics
Thomas Kleinert: Friedrich-Alexander-Universität Erlangen-Nürnberg, Discrete Optimization
Martin Schmidt: Trier University

Journal of Global Optimization, 2022, vol. 84, issue 3, No 5, 685 pages

Abstract: Abstract Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard to solve in theory and practice. In this paper, we add on the general difficulty of this class of problems by further incorporating convex black-box constraints in the lower level. For this setup, we develop a cutting-plane algorithm that computes approximate bilevel-feasible points. We apply this method to a bilevel model of the European gas market in which we use a joint chance constraint to model uncertain loads. Since the chance constraint is not available in closed form, this fits into the black-box setting studied before. For the applied model, we use further problem-specific insights to derive bounds on the objective value of the bilevel problem. By doing so, we are able to show that we solve the application problem to approximate global optimality. In our numerical case study we are thus able to evaluate the welfare sensitivity in dependence of the achieved safety level of uncertain load coverage.

Keywords: Bilevel optimization; Black-box constraints; Chance constraints; Cutting planes; European gas market; 90C90; 90C46; 90B15 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-022-01161-z

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