Haslinger, Jaroslav; Neittaanmäki, Pekka Penalty method in design optimization of systems governed by a unilateral boundary value problem. (English) Zbl 0547.49004 Ann. Fac. Sci. Toulouse, V. Sér., Math. 5, 199-216 (1983). Authors’ summary: ”A method of penalization is used to transform an optimal design problem governed by variational inequalities to an optimal design problem governed by equations. It is shown that the corresponding optimal designs (associated with the penalized problems) are in an appropriate sense close to the optimal design of the original problem.” Reviewer: V.Mustonen Cited in 7 Documents MSC: 49J20 Existence theories for optimal control problems involving partial differential equations 49J40 Variational inequalities 49M30 Other numerical methods in calculus of variations (MSC2010) 93D20 Asymptotic stability in control theory Keywords:penalization; optimal design PDF BibTeX XML Cite \textit{J. Haslinger} and \textit{P. Neittaanmäki}, Ann. Fac. Sci. Toulouse, Math. (5) 5, 199--216 (1983; Zbl 0547.49004) Full Text: DOI Numdam EuDML References: [1] Begis, D., and Glowinski, R.. «Application de la méthode des éléments finis à l’approximation d’un problème de domaine optimal». Appl. Math. Optim.2, 1975, 130-169. · Zbl 0323.90063 [2] Duvaut, G. and Lions, J.L.. «Inequalities in mechanics and physics». Grundlehren der mathematischen Wissenschaften219. Springer-Verlag, Berlin, 1976. · Zbl 0331.35002 [3] Glowinski, R., Lions, J.L. and Tremolieres, R.. «Numerical analysis of variational inequalities». Studies in Mathematics and its Applications8. North-Holland, Amsterdam, 1981. · Zbl 0463.65046 [4] Haslinger, J. and Neittaanmäki, P.. «On optimal shape design of sytems governed by mixed Dirichlet-Signorini boundary value problems». University of Jyväskylä, Dept. Math. preprint 22, 1983. · Zbl 0603.49020 [5] Haug, E.J. and Arora, J.S.. «Applied optimal design, mechanical and structural systems». Wiley-Interscience Publication, New-York, 1979. [6] Haug, E.J. and Cea, J. (ed.). «Optimization of distributed parameter structures». Nato Advances Study Institutes Series, Series E, n° 49, Sijthoff & Noordhoff, Alphen aan den Rijn, 1981. · Zbl 0511.00034 [7] Hlavacek, I. and Nečas, J.. «Optimization of the domain in elliptic unilateral boundary value problems by finite element method». R.A.I.R.O., Num. Anal.16, 1982, 351-373. · Zbl 0496.65057 [8] Kinderlehrer, D. and Stampacchia, G.. «An introduction to variational inequalities and their applications». Pure and Applied Mathematics88, Academic Press, New-York, 1980. · Zbl 0457.35001 [9] Lions, J.L.. «Quelques méthodes de résolution des problèmes aux limites non linéaires». Dunod, Gauthier-Villars, Paris, 1969. · Zbl 0189.40603 [10] Lions, J.L.. «Optimal control of systems governed by partial differential equations». Grundlehren der mathematischen Wissenschaften170. Springer-Verlag, Berlin, 1971. · Zbl 0203.09001 [11] Mignot, F.. «Contrôle dans les inéquations variationnelles elliptiques». J. Funct. Anal.22, 1976, 130-185. · Zbl 0364.49003 [12] Panagiotopoulos, P.D.. «Optimal control in the unilateral thin plate theory, Arch. Mech. Stos.29, 1977, 25-39. · Zbl 0359.73050 [13] Pironneau, O.. «Optimal shape design for elliptic systems». , Springer Verlag, New-York, 1983. · Zbl 0534.49001 [14] Pironneau, O. and Saguez, C.. «Asymptotic behaviour of the solutions of partial differential equations with respect to the domain». IRIA Laboria, rapport n° 218, 1977. [15] Zolesio, J.P.. «The material derivative (or speed) method for shape optimization». I n [6], pp. 1089-1151. · Zbl 0517.73097 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.