Sequential quadratic programming for certain parameter identification problems

We analyze the method of sequential quadratic programming for equality constrained minimization problems in Hilbert spaces of functions, and for the discrete approximations of such problems in the context of an elliptic parameter identification problem. We show how the discretization can be constructed so as to preserve the convergence behavior of the iterates for the infinite dimensional problem in the finite dimensional approximations. We use the structure of the parameter identification problem to reduce the size of the linear system for the SQP step and verify nondegeneracy of the constraints.

[1]  G. R. Walsh,et al.  Methods Of Optimization , 1976 .

[2]  R. Rockafellar.  Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming , 1974 .

[3]  Shih-Ping Han.  A globally convergent method for nonlinear programming , 1975 .

[4]  A. Ioffe.  Necessary and Sufficient Conditions for a Local Minimum. 3: Second Order Conditions and Augmented Duality , 1979 .

[5]  R. Temam,et al.  Navier-Stokes equations: theory and numerical analysis: R. Teman North-Holland, Amsterdam and New York. 1977. 454 pp. US $45.00 , 1978 .

[6]  A. Ioffe.  Necessary and Sufficient Conditions for a Local Minimum. 2: Conditions of Levitin–Miljutin–Osmolovskii Type , 1979 .

[7]  A. Ioffe.  Necessary and Sufficient Conditions for a Local Minimum. 1: A Reduction Theorem and First Order Conditions , 1979 .

[8]  C. Kravaris,et al.  Identification of parameters in distributed parameter systems by regularization , 1983, The 22nd IEEE Conference on Decision and Control.

[9]  P. Boggs,et al.  A family of descent functions for constrained optimization , 1984 .

[10]  C. Kravaris,et al.  Identification of spatially varying parameters in distributed parameter systems by discrete regularization , 1986 .

[11]  Ya-Xiang Yuan,et al.  A recursive quadratic programming algorithm that uses differentiable exact penalty functions , 1986, Math. Program..

[12]  K. Kunisch,et al.  Regularity properties in parameter estimation of diffusion coefficients in one dimensional elliptic boundary value problems , 1986 .

[13]  E. Allgower,et al.  A mesh-independence principle for operator equations and their discretizations , 1986 .

[14]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[15]  K. Kunisch,et al.  The augmented lagrangian method for parameter estimation in elliptic systems , 1990 .