Optimality conditions for bilevel programming problems
From MaRDI portal
Publication:4836753
DOI10.1080/02331939508844060zbMath0820.65032OpenAlexW1983644172MaRDI QIDQ4836753
No author found.
Publication date: 21 June 1995
Published in: Optimization (Search for Journal in Brave)
Full work available at URL: http://hdl.handle.net/1828/2650
nonsmooth analysislinear complementarityoptimality conditionsconstraint qualificationbilevel programming problemcalmness condition
Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Nonsmooth analysis (49J52) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)
Related Items
An SOS1-based approach for solving MPECs with a natural gas market application ⋮ Some new optimality conditions for semivector bilevel optimization program ⋮ Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints ⋮ A new approach to solve convex infinite-dimensional bilevel problems: application to the pollution emission price problem ⋮ Bilevel and multilevel programming: A bibliography review ⋮ Semismooth Newton-type method for bilevel optimization: global convergence and extensive numerical experiments ⋮ Subdifferentials of value functions and optimality conditions for DC and bilevel infinite and semi-infinite programs ⋮ Solving ill-posed bilevel programs ⋮ Solution algorithm for an optimistic linear Stackelberg problem ⋮ Bilevel Optimization: Reformulation and First Optimality Conditions ⋮ Optimality Conditions for Bilevel Programming: An Approach Through Variational Analysis ⋮ Perturbed differential inclusion problems with nonadditive \(L^ 1\)-perturbations and applications ⋮ Estimates of generalized hessians for optimal value functions in mathematical programming ⋮ An aspect of bilevel fixed charge fractional transportation problem ⋮ The natural gas cash-out problem: a bilevel optimal control approach ⋮ A solution method for the optimistic linear semivectorial bilevel optimization problem ⋮ New optimality conditions and a scalarization approach for a nonconvex semi-vectorial bilevel optimization problem ⋮ Imputing a variational inequality function or a convex objective function: a robust approach ⋮ Sufficient optimality conditions using convexifactors for optimistic bilevel programming problem ⋮ Analysis of a new sequential optimality condition applied to mathematical programs with equilibrium constraints ⋮ Solving binary-constrained mixed complementarity problems using continuous reformulations ⋮ Bilevel optimization: on the structure of the feasible set ⋮ Approximate values for mathematical programs with variational inequality constraints ⋮ Approaches to four types of bilevel programming problems with nonconvex nonsmooth lower level programs and their applications to newsvendor problems ⋮ Necessary optimality conditions and a new approach to multiobjective bilevel optimization problems ⋮ Bilevel programming approaches to production planning for multiple products with short life cycles ⋮ New optimality conditions for bilevel programs by using an exact separation principle ⋮ Solving inverse optimal control problems via value functions to global optimality ⋮ Necessary optimality conditions for a semivectorial bilevel optimization problem using the kth-objective weighted-constraint approach ⋮ Optimality conditions for optimistic bilevel programming problem using convexifactors ⋮ Variational analysis of marginal functions with applications to bilevel programming ⋮ Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints ⋮ The generalized Mangasarian-Fromowitz constraint qualification and optimality conditions for bilevel programs ⋮ Relaxed constant positive linear dependence constraint qualification and its application to bilevel programs ⋮ On multiobjective bilevel optimization using tangential subdifferentials ⋮ A Value-Function-Based Exact Approach for the Bilevel Mixed-Integer Programming Problem ⋮ Improved Convergence Properties of the Relaxation Schemes of Kadrani et al. and Kanzow and Schwartz for MPEC ⋮ A primal nonsmooth reformulation for bilevel optimization problems ⋮ Difference of convex algorithms for bilevel programs with applications in hyperparameter selection ⋮ The bilevel programming problem: reformulations, constraint qualifications and optimality conditions ⋮ Optimality and duality results for bilevel programming problem using convexifactors ⋮ A note on optimality conditions for bilevel programming problems∗ ⋮ New optimality conditions for the semivectorial bilevel optimization problem ⋮ On the Guignard constraint qualification for mathematical programs with equilibrium constraints ⋮ Optimal price zones of electricity markets: a mixed-integer multilevel model and global solution approaches ⋮ Necessary optimality conditions for bilevel set optimization problems ⋮ On the Karush-Kuhn-Tucker reformulation of the bilevel optimization problem ⋮ On Lipschitz semicontinuity properties of variational systems with application to parametric optimization ⋮ On solving simple bilevel programs with a nonconvex lower level program ⋮ Is bilevel programming a special case of a mathematical program with complementarity constraints? ⋮ Two-level value function approach to non-smooth optimistic and pessimistic bilevel programs ⋮ Statistics with set-valued functions: applications to inverse approximate optimization ⋮ Smoothing augmented Lagrangian method for nonsmooth constrained optimization problems ⋮ On calmness conditions in convex bilevel programming ⋮ Computing feasible points for binary MINLPs with MPECs ⋮ New Applications of Variational Analysis to Optimization and Control ⋮ Optimality Conditions for Special Semidefinite Bilevel Optimization Problems ⋮ Optimality conditions and duality in terms of convexificators for multiobjective bilevel programming problem with equilibrium constraints ⋮ The global weak sharp minima with explicit exponents in polynomial vector optimization problems ⋮ An equivalent one level optimization problem to a semivectorial bilevel problem ⋮ Unnamed Item ⋮ A relaxation solving approach for the linear trilevel programming problem ⋮ Equivalent Lipschitz surrogates for zero-norm and rank optimization problems ⋮ Computational optimization of gas compressor stations: MINLP models versus continuous reformulations ⋮ An overview of bilevel optimization ⋮ Bilevel road pricing: theoretical analysis and optimality conditions ⋮ Abadie-type constraint qualification for mathematical programs with equilibrium constraints ⋮ Second order optimality conditions for bilevel set optimization problems ⋮ Necessary optimality conditions for bilevel optimization problems using convexificators ⋮ Optimality conditions for nonsmooth generalized semi-infinite programs ⋮ Bilevel Optimal Control Problems with Pure State Constraints and Finite-dimensional Lower Level ⋮ Fuzzy and Exact Optimality Conditions for a Bilevel Set-Valued Problem via Extremal Principles ⋮ Gauss-Newton-type methods for bilevel optimization ⋮ Theoretical and numerical comparison of the Karush-Kuhn-Tucker and value function reformulations in bilevel optimization ⋮ Bilevel Optimal Control With Final-State-Dependent Finite-Dimensional Lower Level ⋮ A Cutting Plane Approach for Solving Linear Bilevel Programming Problems ⋮ Bilevel programming problems with simple convex lower level ⋮ Convergence properties of the inexact Lin-Fukushima relaxation method for mathematical programs with complementarity constraints ⋮ A smoothing augmented Lagrangian method for solving simple bilevel programs ⋮ Monotonicity of Optimal Contracts Without the First-Order Approach ⋮ New uniform parametric error bounds ⋮ Weak via strong Stackelberg problem: New results ⋮ Improved convergence results for a modified Levenberg–Marquardt method for nonlinear equations and applications in MPCC ⋮ Optimality Conditions for a Nonsmooth Semivectorial Bilevel Optimization Problem ⋮ Bilevel convex programming models ⋮ Second order optimality conditions for a bilevel optimization problem in terms of approximate Hessians ⋮ Optimality conditions for vector optimization problems ⋮ Optimality results for a specific bilevel optimization problem ⋮ Necessary optimality conditions for optimistic bilevel programming problems using set-valued programming ⋮ Interactions Between Bilevel Optimization and Nash Games ⋮ Regularization and Approximation Methods in Stackelberg Games and Bilevel Optimization ⋮ Bilevel Optimization and Variational Analysis ⋮ Constraint Qualifications and Optimality Conditions in Bilevel Optimization ⋮ Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography ⋮ Unnamed Item ⋮ A superlinearly convergent implicit smooth SQP algorithm for mathematical programs with nonlinear complementarity constraints ⋮ Sufficient Optimality Conditions in Bilevel Programming ⋮ R-regularity of set-valued mappings under the relaxed constant positive linear dependence constraint qualification with applications to parametric and bilevel optimization ⋮ A maximum principle for a time-optimal bilevel sweeping control problem ⋮ On the solution of convex bilevel optimization problems ⋮ Asymptotic regularity for Lipschitzian nonlinear optimization problems with applications to complementarity constrained and bilevel programming ⋮ Learning with Limited Samples: Meta-Learning and Applications to Communication Systems ⋮ Generic Property of the Partial Calmness Condition for Bilevel Programming Problems ⋮ Distributionally Robust Second-Order Stochastic Dominance Constrained Optimization with Wasserstein Ball ⋮ Directional Necessary Optimality Conditions for Bilevel Programs ⋮ First- and second-order optimality conditions in optimistic bilevel set-valued programming ⋮ Bilevel Polynomial Programs and Semidefinite Relaxation Methods ⋮ Zero-norm regularized problems: equivalent surrogates, proximal MM method and statistical error bound ⋮ A one-layer recurrent neural network for nonsmooth pseudoconvex optimization with quasiconvex inequality and affine equality constraints ⋮ Second-Order Optimality Conditions for General Nonconvex Optimization Problems and Variational Analysis of Disjunctive Systems ⋮ Minimax Problems with Coupled Linear Constraints: Computational Complexity and Duality ⋮ Focus programming: a bi‐level programming approach to static stochastic optimization problems ⋮ Approximate Karush-Kuhn-Tucker condition for multi-objective optimistic bilevel programming problems ⋮ Applying directional upper semi-regular convexificators in bilevel optimization ⋮ Extension of the value function reformulation to multiobjective bilevel optimization ⋮ A survey on mixed-integer programming techniques in bilevel optimization ⋮ Linearly convergent bilevel optimization with single-step inner methods ⋮ A study of mixed discrete bilevel programs using semidefinite and semi-infinite programming ⋮ Estimates for coderivative of solution map in bilevel program ⋮ Levenberg-Marquardt method and partial exact penalty parameter selection in bilevel optimization ⋮ Variational Methods for Emerging Real–Life and Environmental Conservation Problems ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Optimality conditions for a bilevel optimization problem in terms of KKT multipliers and convexificators ⋮ On Lipschitz-like continuity of a class of set-valued mappings ⋮ Efficiency conditions for multiobjective bilevel programming problems via convexificators ⋮ A Lagrange Multiplier Expression Method for Bilevel Polynomial Optimization ⋮ Necessary optimality conditions for a semivectorial bilevel problem under a partial calmness condition ⋮ A new equivalent single-level problem for bilevel problems ⋮ New necessary optimality conditions in optimistic bilevel programming ⋮ Optimality conditions for mixed discrete bilevel optimization problems ⋮ Exact penalty functions for convex bilevel programming problems. ⋮ Gradient-Based Solution Algorithms for a Class of Bilevel Optimization and Optimal Control Problems with a Nonsmooth Lower Level ⋮ Preconditioned proximal point methods and notions of partial subregularity ⋮ Optimality conditions for bilevel programming problems ⋮ Solution of bilevel optimization problems using the KKT approach ⋮ Mathematical Programs with Equilibrium Constraints: A Brief Survey of Methods and Optimality Conditions ⋮ Smoothing SQP Methods for Solving Degenerate Nonsmooth Constrained Optimization Problems with Applications to Bilevel Programs ⋮ Necessary optimality conditions of a D.C. set-valued bilevel optimization problem ⋮ The Price of Inexactness: Convergence Properties of Relaxation Methods for Mathematical Programs with Complementarity Constraints Revisited ⋮ An inertial extrapolation method for convex simple bilevel optimization
Cites Work
- A theoretical approximation scheme for Stackelberg problems
- A simple characterization of solutions sets of convex programs
- Necessary conditions and sufficient conditions for static minmax problems
- Refinements of necessary optimality conditions in nondifferentiable programming. I
- Necessary optimality conditions for Stackelberg problems
- The Fritz John necessary optimality conditions in the presence of equality and inequality constraints
- Weak Sharp Minima in Mathematical Programming
- Optimization and nonsmooth analysis
- A Gauss-Newton Approach to Solving Generalized Inequalities
- A new computational method for Stackelberg and min-max problems by use of a penalty method
- A necessary and a sufficient optimality condition for bilevel programming problems
- Convex Analysis
- On the inverse of matrices with nearly equal elements