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Description: |
We present a new method for the large-scale trust-region subproblem (TRS): minimize a quadratic function subject to a quadratic constraint. The method is matrix-free in the sense that only matrix-vector products are required. The new method is based on a reformulation of the TRS as a parameterized eigenvalue problem. The strategy consists on an iterative procedure that drives the parameter towards its optimal value. The solution to the TRS is then recovered from the solution of the eigenvalue problem corresponding to the optimal parameter. A large-scale eigenvalue problem must be solved at each iteration. This is accomplished by means of the Implicitly Restarted Lanczos Method.
The main features of our method are that it uses the Hessian only in matrix-vector products, has low and fixed storage requirements and handles problems with high degree of singularities, which show in the form of the so-called hard case. This situation arises for example in the regularization of large-scale discrete forms of ill-posed problems.
We will describe the method, discuss the issues associated with ill-posed problems and present numerical results on large-scale discrete ill-posed problems from inverse problems in several areas.
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Date: |
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| Start Time: |
15:00 |
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Speaker: |
Marielba Rojas (CERFACS, Toulouse, France)
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Place: |
Room 5.7
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| Research Groups: |
-Numerical Analysis and Optimization
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See more:
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