First- and second-order optimality conditions for mathematical programs with vanishing constraints.

DOI10.1007/s10492-007-0029-yzbMath1164.90407OpenAlexW1988831514MaRDI QIDQ954637

Christian Kanzow, Tim Hoheisel

Publication date: 24 November 2008

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/33305

zbMATH Keywords

second-order optimality conditionsfirst-order optimality conditionsmathematical programs with equilibrium constraintsmathematical programs with vanishing constraints

Mathematics Subject Classification ID

Nonlinear programming (90C30) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)

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Cites Work

• Unnamed Item
• Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints
• Mathematical programs with vanishing constraints: optimality conditions and constraint qualifications
• Nonsmooth approach to optimization problems with equilibrium constraints. Theory, applications and numerical results
• Stationary conditions for mathematical programs with vanishing constraints using weak constraint qualifications
• Convergence Properties of a Regularization Scheme for Mathematical Programs with Complementarity Constraints
• Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
• A direct proof for M-stationarity under MPEC-GCQ for mathematical programs with equilibrium constraints
• On the Abadie and Guignard constraint qualifications for Mathematical Programmes with Vanishing Constraints
• Nonconvex Structures in Nonlinear Programming
• Optimality Conditions for a Class of Mathematical Programs with Equilibrium Constraints
• Mathematical Programs with Equilibrium Constraints