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Sequential quadratic programming for certain parameter identification problems. (English) Zbl 0743.65070

The authors show how the method of sequential quadratic programming can be applied to elliptic parameter identification problems (and their large scale finite dimensional discretizations) by treating in detail the following problem: To estimate the coefficient function \(q(x)\) in the one-dimensional elliptic equation \(-(qu')'=f\) in \(I\), \(I\) denoting the unit interval in \(R\), with \(u=0\) on the boundary, provided the function \(f(x)\) and an observation \(z(x)\) of \(u\) in \(I\) are known.
The paper also contains a discussion of implementation aspects of the proposed method as well as a presentation of some numerical results.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
90C20 Quadratic programming
34A55 Inverse problems involving ordinary differential equations
65K10 Numerical optimization and variational techniques
34B05 Linear boundary value problems for ordinary differential equations
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