Iterative Solution Methods for a Class of State and Control Constrained Optimal Control Problems

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References

[1] J.-L. Lions, “Optimal Control of Systems Gouverhed by Partial Differential Equations,” Springer-Verlag, New York, 1971. doi:10.1007/978-3-642-65024-6

[2] P. Neittaanmaki, J. Sprekels and D. Tiba, “Optimization of Elliptic Systems. Theory and Applications,” SpringerVerlag, New York, 2006.

[3] P. H. Ciarlet and J.-L. Lions, “Handbook of Mumerical Analysis: Finite Element Methods,” North-Holland, Amsterdam, 1991.

[4] A. Lapin, “Preconditioned Uzawa-Type Methods for Finite-Dimensional Constrained Saddle Point Problems,” Lobachevskii Journal of Mathematics, Vol. 31, No. 4, 2010, pp. 309-322.

[5] R. Glowinski, J.-L. Lions and R. Tremolieres, “Numeral Analysis of Variational Inequalities,” Translated and Re-vised Edition, North-Holland Publishing Company, Amsterdam, New York and Oxford, 1981.

[6] A. Lapin, “Iterative Solution Methods for Mesh Variational Inequalities,” Kazan State University, Kazan, 2008.

[7] I. Hlavac?k, J. Haslinger, J. Nec?s and J. Lovis?k, “Solution of Variational Inequalities in Mechanics,” Springer Verlag, New York, 1988.

[8] A. V. Lapin, “Methods of Upper Relaxation Type for the Sum of a Quadratic and a Convex Functional,” Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, No. 8, 1993, pp. 30-39.

[9] A. Lapin and M. Khasanov, “State-Constrained Optimal Control of an Elliptic Equation with Its Right-Hand Side Used as Control Function,” Lobachevskii Journal of Mathematics, Vol. 32, No. 4, 2011, pp. 453-462.
doi:10.1134/S1995080211040287

[10] E. Laitinen and A. Lapin, “Iterative Solution Methods for the Large Scale Constrained Saddle Point Problems,” In: S. Repin, T. Tiihonen and T. Tuovinen, Eds., Numerical Methods for Differential Equations, Optimization, and Technological Problems, Springer, New York, 2012, pp. 19-39.