3,863 research outputs found
Computational complexity of ÎĽ calculation
The structured singular value ÎĽ measures the robustness of uncertain systems. Numerous researchers over the last decade have worked on developing efficient methods for computing ÎĽ. This paper considers the complexity of calculating ÎĽ with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the ÎĽ recognition problem with either pure real or mixed real/complex uncertainty is NP-hard. This strongly suggests that it is futile to pursue exact methods for calculating ÎĽ of general systems with pure real or mixed uncertainty for other than small problems
A Method to Guarantee Local Convergence for Sequential Quadratic Programming with Poor Hessian Approximation
Sequential Quadratic Programming (SQP) is a powerful class of algorithms for
solving nonlinear optimization problems. Local convergence of SQP algorithms is
guaranteed when the Hessian approximation used in each Quadratic Programming
subproblem is close to the true Hessian. However, a good Hessian approximation
can be expensive to compute. Low cost Hessian approximations only guarantee
local convergence under some assumptions, which are not always satisfied in
practice. To address this problem, this paper proposes a simple method to
guarantee local convergence for SQP with poor Hessian approximation. The
effectiveness of the proposed algorithm is demonstrated in a numerical example
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