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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 69, 2020 - Issue 5
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Articles

Solvability and optimization for a class of mixed variational problems

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Pages 1097-1116 | Received 02 May 2019, Accepted 22 Sep 2019, Published online: 20 Oct 2019

References

  • Céa J. Optimization. Théorie et algorithmes. Paris: Dunod; 1971.
  • Glowinski R, Lions JL, Trémolières R. Numerical analysis of variational inequalities. Amsterdam: North-Holland; 1981.
  • Haslinger J, Hlaváček I, Nečas J. Numerical Methods for Unilateral Problems in Solid Mechanics, In Lions J.L. and Ciarlet P.G. editors. Handbook of Numerical Analysis, Vol. IV, pp. 313–485. Amsterdam: North-Holland; 1996.
  • Hlaváček I, Haslinger J, Nečas J, et al. Solution of variational inequalities in mechanic. New York: Springer-Verlag; 1988.
  • Reddy BD. Mixed variational inequalities arising in elastoplasticity. Nonlinear Anal. 1992;19:1071–1089. doi: 10.1016/0362-546X(92)90125-X
  • Amdouni S, Hild P, Lleras V, et al. A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies. ESAIM M2AN Math Model Numer Anal. 2012;46:813–839. doi: 10.1051/m2an/2011072
  • Barboteu M, Matei A, Sofonea M. Analysis of quasistatic viscoplastic contact problems with normal compliance. Quart J Mech Appl Math. 2012;65:555–579. doi: 10.1093/qjmam/hbs016
  • Hild P, Renard Y. A stabilized Lagrange multiplier method for the finite element approximation of contact problems in elastostatics. Numer Math. 2010;115:101–129. doi: 10.1007/s00211-009-0273-z
  • Hüeber S, Matei A, Wohlmuth B. A mixed variational formulation and an optimal a priori error estimate for a frictional contact problem in elasto-piezoelectricity. Bull Math Soc Sci Math Roumanie. 2005;48:209–232.
  • Hüeber S, Matei A, Wohlmuth B. Efficient algorithms for problems with friction. SIAM J Sci Comput. 2007;29:70–92. doi: 10.1137/050634141
  • Sofonea M, Matei A, Xiao YB. Optimal control for a class of mixed variational problems. Math. phys. 2019; 70(127). https://doi.org/10.1007/s00033-019-1173-4.
  • Matei A. A mixed hemivariational-variational problem and applications. Comp Math Appl. 2019;77(11):2989–3000. doi: 10.1016/j.camwa.2018.08.068
  • Matei A, Micu S, Niţă C. Optimal control for antiplane frictional contact problems involving nonlinearly elastic materials of Hencky-type. Math Mech Solids. 2018;23:308–328. doi: 10.1177/1081286517718605
  • Barbu V. Optimal control of variational inequalities. Boston: Pitman; 1984.
  • Lions J-L. Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles. Paris: Dunod; 1968.
  • Neitaanmaki P, Sprekels J, Tiba D. Optimization of elliptic systems: theory and applications. Springer Monographs in Mathematics. New York: Springer; 2006.
  • Tiba D. Lectures on the optimal control of elliptic equations. Lecture Notes. Vol. 32. University of Jyväskylä, Jyväskylä; 1995.
  • Tiba D. Optimal control of nonsmooth distributed parameter systems. Berlin: Springer; 1990.
  • Freidman A. Optimal control for variational inequalities. SIAM J Control Opt. 1986;24:439–451. doi: 10.1137/0324025
  • Liu ZH, Zeng B. Optimal control of generalized quasi-variational hemivariational inequalities and its applications. Appl Math Optim. 2015;72:305–323. doi: 10.1007/s00245-014-9281-1
  • Mignot R. Contrôle dans les inéquations variationnelles elliptiques. J Func Anal. 1976;22:130–185. doi: 10.1016/0022-1236(76)90017-3
  • Mignot F, Puel J-P. Optimal control in some variational inequalities. SIAM J Control Opt. 1984;22:466–476. doi: 10.1137/0322028
  • Sofonea M. Convergence results and optimal control for a class of hemivariational inequalities. SIAM J Math Anal. 2018;50:4066-–4086. doi: 10.1137/17M1144404
  • Sofonea M, Matei A. Variational inequalities with applications. A study of antiplane frictional contact problems. Advances in Mechanics and Mathematics. Vol. 18. New York: Springer; 2009.
  • Dinca G, Jebelean P, Mawhin J. Variational and topological methods for Dirichlet problems with p-Laplacian. Portugalie Mathematica. 2001;58(3):339. Nova Série.
  • Glowinski R, Marrocco A. Sur l'approximation par éléments finits d'ordre un, et la résolution par penalisation-dualité d'une classe de problèmes de Dirichlet non linéaires. RAIRO Anal Numer. 1975;2:41–76.
  • Matei A. An existence result for a mixed variational problem arising from contact mechanics. Nonlinear Anal Ser B Real World Appl. 2014;20:74–81. doi: 10.1016/j.nonrwa.2014.01.010

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