Second order optimality conditions for a bilevel optimization problem in terms of approximate Hessians

DOI10.1016/j.jmaa.2021.125932zbMath1486.90184OpenAlexW4200601883MaRDI QIDQ2069774

Stephan Dempe, Nazih Abderrazzak Gadhi, M. El Idrissi

Publication date: 21 January 2022

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2021.125932

zbMATH Keywords

constraint qualificationapproximate HessianKKT conditionsbilevel optimizationsecond order optimality conditions

Mathematics Subject Classification ID

Nonlinear programming (90C30) Optimality conditions and duality in mathematical programming (90C46)

Cites Work

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• Is bilevel programming a special case of a mathematical program with complementarity constraints?
• Generalized Hessian matrix and second-order optimality conditions for problems with \(C^{1,1}\) data
• Some properties of the bilevel programming problem
• Necessary optimality conditions for bilevel set optimization problems
• Second-order necessary conditions of the Kuhn-Tucker type under new constraint qualifications
• Second-order optimality conditions in multiobjective optimization problems
• Necessary optimality conditions for Stackelberg problems
• Generalized differential calculus for nonsmooth and set-valued mappings
• Necessary optimality conditions for bilevel optimization problems using convexificators
• Second Order Optimality Conditions for Problems with Continuously Differentiable Data
• A unified theory of first and second order conditions for extremum problems in topological vector spaces
• Approximate Jacobian Matrices for Nonsmooth Continuous Maps and C¹-Optimization
• Approximate Hessian matrices and second-order optimality conditions for nonlinear programming problems with C¹-data
• Problems of Hierarchical Optimization in Finite Dimensions
• A necessary and a sufficient optimality condition for bilevel programming problems
• A Sharp Lagrange Multiplier Rule for Nonsmooth Mathematical Programming Problems Involving Equality Constraints
• Optimality conditions for bilevel programming problems