The nonlinear bilevel programming problem:formulations,regularity and optimality conditions

DOI10.1080/02331939508844048zbMath0817.90101OpenAlexW2033573391MaRDI QIDQ4764597

Yao Chen, Michael Florian

Publication date: 8 May 1995

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331939508844048

zbMATH Keywords

nonlinear bilevel programmingnondifferential optimizationFritz-John type optimality conditionsregularity and optimality conditions

Mathematics Subject Classification ID

Nonlinear programming (90C30) Nonsmooth analysis (49J52)

Related Items

Smoothing and regularization strategies for optimization of hybrid dynamic systems, Bilevel and multilevel programming: A bibliography review, Numerical Methods for Diagnosis and Therapy Design of Cerebral Palsy by Bilevel Optimal Control of Constrained Biomechanical Multi-Body Systems, Models and a relaxation algorithm for continuous network design problem with a tradable credit scheme and equity constraints, A class of smoothing methods for mathematical programs with complementarity constraints, Expected residual minimization formulation for a class of stochastic linear second-order cone complementarity problems, Models and Software for Urban and Regional Transportation Planning: The Contributions of the Center for Research on Transportation, The quasiparticle lifetime in a doped graphene sheet, New relaxation method for mathematical programs with complementarity constraints, Model Order Reduction Techniques with a Posteriori Error Control for Nonlinear Robust Optimization Governed by Partial Differential Equations, Necessary optimality conditions for mathematical programs with second-order cone complementarity constraints, On the Karush-Kuhn-Tucker reformulation of the bilevel optimization problem, Exact penalization and necessary optimality conditions for multiobjective optimization problems with equilibrium constraints, A projection-based reformulation and decomposition algorithm for global optimization of a class of mixed integer bilevel linear programs, Multilevel (Hierarchical) Optimization: Complexity Issues, Optimality Conditions, Algorithms, An MPEC formulation and its cutting constraint algorithm for continuous network design problem with multi-user classes, Newton-type method for a class of mathematical programs with complementarity constraints, Stochastic mathematical programs with hybrid equilibrium constraints, Combined Monte Carlo sampling and penalty method for Stochastic nonlinear complementarity problems, A smoothing heuristic for a bilevel pricing problem, Optimization problems for machine learning: a survey, Regularization method for stochastic mathematical programs with complementarity constraints, Two approaches for solving mathematical programs with second-order cone complementarity constraints, On M-stationary points for mathematical programs with equilibrium constraints, KKT transformation approach for multi-objective multi-level linear programming problems, Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography

Cites Work

• On the structure and properties of a linear multilevel programming problem
• A sequential LCP method for bilevel linear programming
• The steepest descent direction for the nonlinear bilevel programming problem
• Optimality conditions for the bilevel programming problem
• Directional differentiability of the optimal value function in a nonlinear programming problem
• An Algorithm for Solving the General Bilevel Programming Problem
• Optimization and nonsmooth analysis
• A note on the optimality conditions for the bilevel programming problem
• On two-level optimization
• New Branch-and-Bound Rules for Linear Bilevel Programming
• Two-Level Linear Programming
• Constraint qualifications in maximization problems
• Convex Analysis
• A solution method for the linear static Stackelberg problem using penalty functions
• Unnamed Item