Weak and strong stationarity in generalized bilevel programming and bilevel optimal control

DOI10.1080/02331934.2015.1122007zbMath1367.90120OpenAlexW2276758637MaRDI QIDQ2810101

Gerd Wachsmuth, Patrick Mehlitz

Publication date: 31 May 2016

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331934.2015.1122007

zbMATH Keywords

stationaritybilevel programmingmathematical program with complementarity constraintsbilevel optimal controlprogramming in Banach spaces

Mathematics Subject Classification ID

Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Programming in abstract spaces (90C48) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Optimality conditions for problems involving ordinary differential equations (49K15)

Related Items (21)

Analysis and Solution Methods for Bilevel Optimal Control Problems ⋮ Extensions of Nash Games in Finite and Infinite Dimensions with Applications ⋮ Optimal Control Problems with Terminal Complementarity Constraints ⋮ A non-convex denoising model for impulse and Gaussian noise mixture removing using bi-level parameter identification ⋮ The limiting normal cone to pointwise defined sets in Lebesgue spaces ⋮ Comparison of optimality systems for the optimal control of the obstacle problem ⋮ Finding global solutions of some inverse optimal control problems using penalization and semismooth Newton methods ⋮ Solving inverse optimal control problems via value functions to global optimality ⋮ Optimal control of a non-smooth semilinear elliptic equation ⋮ New Constraint Qualifications for Optimization Problems in Banach Spaces Based on Asymptotic KKT Conditions ⋮ Optimality conditions for a class of inverse optimal control problems with partial differential equations ⋮ Optimality conditions for the simple convex bilevel programming problem in Banach spaces ⋮ The limiting normal cone of a complementarity set in Sobolev spaces ⋮ New Constraint Qualifications for Mathematical Programs with Equilibrium Constraints via Variational Analysis ⋮ Theoretical and numerical comparison of the Karush-Kuhn-Tucker and value function reformulations in bilevel optimization ⋮ Gradient-Based Solution Algorithms for a Class of Bilevel Optimization and Optimal Control Problems with a Nonsmooth Lower Level ⋮ Optimal control problems with control complementarity constraints: existence results, optimality conditions, and a penalty method ⋮ Bilevel Optimization and Variational Analysis ⋮ Bilevel Optimal Control: Existence Results and Stationarity Conditions ⋮ BOLIB: Bilevel Optimization LIBrary of Test Problems ⋮ Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography

Cites Work

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• Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints
• On the Karush-Kuhn-Tucker reformulation of the bilevel optimization problem
• Is bilevel programming a special case of a mathematical program with complementarity constraints?
• Regularity and stability for the mathematical programming problem in Banach spaces
• Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints
• Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
• Bilevel Optimal Control Problems with Pure State Constraints and Finite-dimensional Lower Level
• Bilevel Optimal Control With Final-State-Dependent Finite-Dimensional Lower Level
• Estimating Parameters in Optimal Control Problems
• Real-Time Solution of Bi-Level Optimal Control Problems
• A direct proof for M-stationarity under MPEC-GCQ for mathematical programs with equilibrium constraints
• Optimal Strategies For Bilevel Dynamic Problems
• Optimality Conditions for Optimization Problems with Complementarity Constraints
• Semivectorial Bilevel Convex Optimal Control Problems: Existence Results

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