Superlinear Convergence of a Stabilized SQP Method to a Degenerate Solution
Computational Optimization and Applications
Stabilized Sequential Quadratic Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Inexact SQP Interior Point Methods and Large Scale Optimal Control Problems
SIAM Journal on Control and Optimization
Test Examples for Nonlinear Programming Codes
Test Examples for Nonlinear Programming Codes
Parallel Variable Distribution for Constrained Optimization
Computational Optimization and Applications
Analysis of Inexact Trust-Region SQP Algorithms
SIAM Journal on Optimization
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
SIAM Journal on Optimization
An Interior Point Algorithm for Large-Scale Nonlinear Programming
SIAM Journal on Optimization
Modifying SQP for Degenerate Problems
SIAM Journal on Optimization
On the Implementation of an Algorithm for Large-Scale Equality Constrained Optimization
SIAM Journal on Optimization
SQP Methods for Large-Scale Nonlinear Programming
Proceedings of the 19th IFIP TC7 Conference on System Modelling and Optimization: Methods, Theory and Applications
SIAM Journal on Optimization
Sequential quadratic programming methods based on indefinite hessian approximations
Sequential quadratic programming methods based on indefinite hessian approximations
On the Sequential Quadratically Constrained Quadratic Programming Methods
Mathematics of Operations Research
A Globally Convergent Linearly Constrained Lagrangian Method for Nonlinear Optimization
SIAM Journal on Optimization
Mathematics of Operations Research
Numerical Optimization: Theoretical and Practical Aspects (Universitext)
Numerical Optimization: Theoretical and Practical Aspects (Universitext)
Computational Optimization and Applications
An Inexact SQP Method for Equality Constrained Optimization
SIAM Journal on Optimization
Mathematical Programming: Series A and B
An inexact Newton method for nonconvex equality constrained optimization
Mathematical Programming: Series A and B
A New Unblocking Technique to Warmstart Interior Point Methods Based on Sensitivity Analysis
SIAM Journal on Optimization
Mathematical Programming: Series A and B
Sharp Primal Superlinear Convergence Results for Some Newtonian Methods for Constrained Optimization
SIAM Journal on Optimization
A line search filter algorithm with inexact step computations for equality constrained optimization
Applied Numerical Mathematics
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We consider sequential quadratic programming (SQP) methods applied to optimization problems with nonlinear equality constraints and simple bounds. In particular, we propose and analyze a truncated SQP algorithm in which subproblems are solved approximately by an infeasible predictor-corrector interior-point method, followed by setting to zero some variables and some multipliers so that complementarity conditions for approximate solutions are enforced. Verifiable truncation conditions based on the residual of optimality conditions of subproblems are developed to ensure both global and fast local convergence. Global convergence is established under assumptions that are standard for linesearch SQP with exact solution of subproblems. The local superlinear convergence rate is shown under the weakest assumptions that guarantee this property for pure SQP with exact solution of subproblems, namely, the strict Mangasarian-Fromovitz constraint qualification and second-order sufficiency. Local convergence results for our truncated method are presented as a special case of the local convergence for a more general perturbed SQP framework, which is of independent interest and is applicable even to some algorithms whose subproblems are not quadratic programs. For example, the framework can also be used to derive sharp local convergence results for linearly constrained Lagrangian methods. Preliminary numerical results confirm that it can be indeed beneficial to solve subproblems approximately, especially on early iterations.