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Numerical Functional Analysis and Optimization Volume 12, 1991 - Issue 5-6
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Original Articles

Approximating optimal controls for elliptic obstacle problem by monotone iteration schemes

Viorel Barbu Department of Mathematical Sciences, Institute for Dynamics and, University of Cincinnati, Cincinnati, Ohio, 45221-0025
&
Philip Korman Department of Mathematical Sciences, Institute for Dynamics and, University of Cincinnati, Cincinnati, Ohio, 45221-0025
Pages 429-442 | Published online: 15 May 2007

References

  • Barbu , V. 1981 . Necessary conditions for nonconvex distributed control problems governed by elliptic variational inequalities . J. Math. Anal. Appl. , 80 : 566 – 597 .
  • Barbu , V. 1984 . Optimal Control of Variational Inequalities , London, Boston, Melbourne : Pitman .
  • Friedman , A. 1987 . Optimal control of elliptic variational inequalities . SIAMJ. Control & Optimiz. , 25
  • Glowinski , R. , Lions , J. L. and Tremolieres , R. 1981 . Numerical Analysis of Variational Inequalities , North-Holland .
  • Huy , C. U. , McKenna , P. J. and Walter , W. 1986 . Finite difference approximations to the Dirichlet problem for elliptic systems $title:Numer. Math. . Numer. Math. , 49 : 227 – 237 .
  • Korman , P. 1989 . On computation of solutions of elliptic systems . Numer. Fund. Anal. and Optimiz. , 10 ( 9 & 10 ) : 977 – 990 .
  • Korman , P. , Leung , A.W. and Stojanovic , S. 1990 . Monotone iterations for nonlinear obstacle problem . J. Austral. Math. Soc. Ser. , B 31 ( 9 & 10 ) : 259 – 276 .
  • Mignot , F. 1976 . Controle dans les inéqualities variationnelles elliptiques . J. Fund. Anal. , 22 ( 9 & 10 ) : 130 – 185 .
  • Sinestrari , E. 1976 . Accretive differential operators . Boll. Unione Mat. Ital. , 75 ( 9 & 10 ) : 19 – 31 .
  • Smith , G. D. 1989 . Numerical Solution of Partial Differential Equations: Finite Difference Methods , Oxford University Press .
  • Stampacchia , G. 1965 . Le Probl$egrave;me de Dirichlet pour les $eacute;quations elliptiques du second . Ann. Inst. Fourier , 15 : 189 – 258 .

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