Tuesday, 15:45 - 16:10 h, Room: H 0110

 

Philip Gill
Regularization and convexification for SQP methods

Coauthor: Daniel P. Robinson

 

Abstract:
We describe a sequential quadratic programming (SQP) method for nonlinear programming that uses a primal-dual generalized augmented Lagrangian merit function to ensure global convergence. Each major iteration involves the solution of a bound-constrained subproblem defined in terms of both the primal and dual variables. A convexification method is used to give a subproblem that is equivalent to a regularized convex quadratic program (QP).
The benefits of this approach include the following: (1) The QP subproblem always has a known feasible point. (2) A projected gradient method may be used to identify the QP active set when far from the solution. (3) The application of a conventional active-set method to the bound-constrained subproblem involves the solution of a sequence of regularized KKT systems. (4) Additional regularization may be applied by imposing explicit bounds on the dual variables. (5) The method is equivalent to the stabilized SQP method in the neighborhood of a solution.

 

Talk 2 of the invited session Tue.3.H 0110
"Recent advances in nonlinear optimization" [...]
Cluster 16
"Nonlinear programming" [...]

 

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