A recursive quadratic programming algorithm that uses differentiable exact penalty functions
Mathematical Programming: Series A and B
A strategy for global convergence in a sequential quadratic programming algorithm
SIAM Journal on Numerical Analysis
A tool for the analysis of Quasi-Newton methods with application to unconstrained minimization
SIAM Journal on Numerical Analysis
Exact penalty function algorithm with simple updating of the penalty parameter
Journal of Optimization Theory and Applications
An analysis of reduced Hessian methods for constrained optimization
Mathematical Programming: Series A and B
Convergence of the BFGS Method for LC1 Convex Constrained Optimization
SIAM Journal on Control and Optimization
Test Examples for Nonlinear Programming Codes
Test Examples for Nonlinear Programming Codes
Practical Update Criteria for Reduced Hessian SQP: Global Analysis
SIAM Journal on Optimization
On the Global Convergence of the BFGS Method for Nonconvex Unconstrained Optimization Problems
SIAM Journal on Optimization
On the Sequential Quadratically Constrained Quadratic Programming Methods
Mathematics of Operations Research
A reduced Hessian SQP method for inequality constrained optimization
Computational Optimization and Applications
Journal of Computational and Applied Mathematics
A regularized limited memory BFGS method for nonconvex unconstrained minimization
Numerical Algorithms
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Sequential quadratic programming (SQP) algorithms have proven to be efficient for solving nonlinearly constrained optimization problems under some conditions. In analysis of global convergence for SQP algorithms, it is usually assumed that the quasi-Newton matrices, approximating the Hessian of Lagrangian function, are uniformly positive definite. However, it is not known whether this condition is satisfied for quasi-Newton matrices. In this paper, we present a new update criterion for the quasi-Newton matrix and a new update method for the penalty parameter. We establish the global convergence result of a modifying SQP algorithm for equality constrained optimization problems without any assumption on quasi-Newton matrix sequence. Moreover, if the second-order sufficient condition holds at an optimal solution, the new update criterion reduces to the ordinary BFGS update. The superlinear rate of convergence of the algorithm can be obtained if an additional step is performed.