Using the KKT matrix in an augmented Lagrangian SQP method for sparse constrained optimization

1995 ◽  
Vol 85 (1) ◽  
pp. 201-220 ◽  
Author(s):  
M. C. Bartholomew-Biggs ◽  
M. De F. G. Hernandez
Keyword(s):  
Constrained Optimization ◽  
Augmented Lagrangian ◽  
Sqp Method

scholarly journals An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems

2021 ◽  
Author(s):  
Christian Kanzow ◽  
Andreas B. Raharja ◽  
Alexandra Schwartz
Keyword(s):  
Constrained Optimization ◽  
Numerical Experiments ◽  
Penalty Method ◽  
Augmented Lagrangian ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Augmented Lagrangian Method ◽  
Constrained Optimization Problems ◽  
Strongly Stationary ◽  
Type Constraint

AbstractA reformulation of cardinality-constrained optimization problems into continuous nonlinear optimization problems with an orthogonality-type constraint has gained some popularity during the last few years. Due to the special structure of the constraints, the reformulation violates many standard assumptions and therefore is often solved using specialized algorithms. In contrast to this, we investigate the viability of using a standard safeguarded multiplier penalty method without any problem-tailored modifications to solve the reformulated problem. We prove global convergence towards an (essentially strongly) stationary point under a suitable problem-tailored quasinormality constraint qualification. Numerical experiments illustrating the performance of the method in comparison to regularization-based approaches are provided.

A subspace SQP method for equality constrained optimization

2019 ◽  
Vol 74 (1) ◽  
pp. 177-194 ◽  
Author(s):  
Jae Hwa Lee ◽  
Yoon Mo Jung ◽  
Ya-xiang Yuan ◽  
Sangwoon Yun
Keyword(s):  
Constrained Optimization ◽  
Sqp Method ◽  
Equality Constrained Optimization
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