Mathematical programs with semidefinite cone complementarity constraints: constraint qualifications and optimality conditions

DOI10.1007/s11228-013-0242-7zbMath1296.90118OpenAlexW2095429996MaRDI QIDQ456990

Yi Zhang, Jia Wu, Li-wei Zhang

Publication date: 26 September 2014

Published in: Set-Valued and Variational Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11228-013-0242-7

zbMATH Keywords

constraint qualificationssecond-order sufficient conditionsB-stationary conditionmathematical program with semidefinite cone complementarity constraints

Mathematics Subject Classification ID

Semidefinite programming (90C22) Nonlinear programming (90C30) Optimality conditions and duality in mathematical programming (90C46)

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Cites Work

• Unnamed Item
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• First order optimality conditions for mathematical programs with semidefinite cone complementarity constraints
• Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints
• Foundations of bilevel programming
• A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities
• Abadie-type constraint qualification for mathematical programs with equilibrium constraints
• Semismoothness of solutions to generalized equations and the Moreau-Yosida regularization
• Robust Convex Optimization
• First Order Conditions for General Nonlinear Optimization
• Variational Analysis
• A Squared Smoothing Newton Method for Nonsmooth Matrix Equations and Its Applications in Semidefinite Optimization Problems
• Second Order Optimality Conditions Based on Parabolic Second Order Tangent Sets
• The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications
• Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints
• Semismooth Matrix-Valued Functions
• Mathematical Programs with Equilibrium Constraints