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1.	Hansson, Anders, et al. (author) Comparison of Two Structure-Exploiting Optimization Algorithms for Integral Quadratic Constraints 2003 In: Proceedings of the 4th IFAC symposium on Robust Control Design. - Linköping : Linköping University Electronic Press. - 9780080440125 Conference paper (peer-reviewed)abstract As the semidefinite programs that result from integral quadratic contstraints are usually large it is important to implement efficient algorithms. The interior-point algorithms in this paper are primal-dual potential reduction methods and handle multiple constraints. Two approaches are made. For the first approach the computational cost is dominated by a least-squares problem that has to be solved in each iteration. The least squares problem is solved using an iterative method, namely the conjugate gradient method. The computational effort for the second approach is dominated by forming a linear system of equations. This systems of equations is used to compute the search direction in each iteration. If the number of variables are reduced by solving a smaller subproblem the resulting system has a very nice structure and can be solved efficiently. The first approach is more efficient for larger problems but is not as numerically stable.

Hansson, Anders, et al. (author)
Comparison of Two Structure-Exploiting Optimization Algorithms for Integral Quadratic Constraints
2003
In: Proceedings of the 4th IFAC symposium on Robust Control Design. - Linköping : Linköping University Electronic Press. - 9780080440125
Conference paper (peer-reviewed)abstract
- As the semidefinite programs that result from integral quadratic contstraints are usually large it is important to implement efficient algorithms. The interior-point algorithms in this paper are primal-dual potential reduction methods and handle multiple constraints. Two approaches are made. For the first approach the computational cost is dominated by a least-squares problem that has to be solved in each iteration. The least squares problem is solved using an iterative method, namely the conjugate gradient method. The computational effort for the second approach is dominated by forming a linear system of equations. This systems of equations is used to compute the search direction in each iteration. If the number of variables are reduced by solving a smaller subproblem the resulting system has a very nice structure and can be solved efficiently. The first approach is more efficient for larger problems but is not as numerically stable.

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