The limiting normal cone of a complementarity set in Sobolev spaces

DOI10.1080/02331934.2018.1484467zbMath1407.49010OpenAlexW2884179907WikidataQ129487121 ScholiaQ129487121MaRDI QIDQ4646519

Gerd Wachsmuth, Felix Harder

Publication date: 14 January 2019

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331934.2018.1484467

zbMATH Keywords

optimality conditionsobstacle problemlimiting normal coneM-stationaritycomplementarity set

Mathematics Subject Classification ID

Existence theories for problems in abstract spaces (49J27) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Optimality conditions (49K99)

Related Items (11)

M-stationarity for a class of MPCCs in Lebesgue spaces ⋮ Analysis and Solution Methods for Bilevel Optimal Control Problems ⋮ Stability and Sensitivity Analysis for Quasi-Variational Inequalities ⋮ An augmented Lagrangian method for optimization problems with structured geometric constraints ⋮ Solving inverse optimal control problems via value functions to global optimality ⋮ The limiting normal cone of a complementarity set in Sobolev spaces ⋮ Optimal control problems with control complementarity constraints: existence results, optimality conditions, and a penalty method ⋮ On the sequential normal compactness condition and its restrictiveness in selected function spaces ⋮ Coupled versus decoupled penalization of control complementarity constraints ⋮ Bilevel Optimal Control: Existence Results and Stationarity Conditions ⋮ Calmness and calculus: two basic patterns

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Several approaches for the derivation of stationarity conditions for elliptic MPECs with upper-level control constraints
• Mathematical programs with complementarity constraints in Banach spaces
• On optimality conditions in control of elliptic variational inequalities
• On sharp necessary optimality conditions in control of contact problems with strings
• Applied functional analysis. Functional analysis, Sobolev spaces and elliptic differential equations
• Contrôle dans les inéquations variationelles elliptiques
• Towards M-stationarity for Optimal Control of the Obstacle Problem with Control Constraints
• Weak and strong stationarity in generalized bilevel programming and bilevel optimal control
• First-Order Optimality Conditions for Elliptic Mathematical Programs with Equilibrium Constraints via Variational Analysis
• Variational Analysis in Sobolev andBVSpaces
• Mathematical Programs with Complementarity Constraints in Function Space: C- and Strong Stationarity and a Path-Following Algorithm
• Optimality conditions for the simple convex bilevel programming problem in Banach spaces
• The limiting normal cone of a complementarity set in Sobolev spaces
• Optimality Conditions for a Class of Mathematical Programs with Equilibrium Constraints
• Strong Stationarity for Optimal Control of the Obstacle Problem with Control Constraints
• Convergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraints
• Comparison of optimality systems for the optimal control of the obstacle problem

This page was built for publication: The limiting normal cone of a complementarity set in Sobolev spaces