Structural and Multidisciplinary Optimization
Mathematical programs with vanishing constraints: critical point theory
Journal of Global Optimization
Solving stress constrained problems in topology and material optimization
Structural and Multidisciplinary Optimization
Active-set Newton methods for mathematical programs with vanishing constraints
Computational Optimization and Applications
Shape equilibrium constraint: a strategy for stress-constrained structural topology optimization
Structural and Multidisciplinary Optimization
A smoothing-regularization approach to mathematical programs with vanishing constraints
Computational Optimization and Applications
Structural and Multidisciplinary Optimization
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We consider a difficult class of optimization problems that we call a mathematical program with vanishing constraints. Problems of this kind arise in various applications including optimal topology design problems of mechanical structures. We show that some standard constraint qualifications like LICQ and MFCQ usually do not hold at a local minimum of our program, whereas the Abadie constraint qualification is sometimes satisfied. We also introduce a suitable modification of the standard Abadie constraint qualification as well as a corresponding optimality condition, and show that this modified constraint qualification holds under fairly mild assumptions. We also discuss the relation between our class of optimization problems with vanishing constraints and a mathematical program with equilibrium constraints.