Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-12T12:52:35.923Z Has data issue: false hasContentIssue false

The extension of optimisation problems containing controls in the coefficients

Published online by Cambridge University Press:  14 November 2011

K. A. Lurie
Affiliation:
Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609-2280, U.S.A.

Synopsis

The paper suggests a procedure for direct construction of minimal extensions of constrained optimisation problems, particularly those containing controls in coefficients of elliptic equations. The preliminary version of the procedure has been described in [1].

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Lurie, K. A.. On the non-self-adjoint problems of optimal control in coefficients of elliptical equations (Preprint-1175, A. F. Ioffe Physical-Technical Institute, Academy of Sciences of the U.S.S.R., Leningrad, 1987) (in Russian).Google Scholar
2Lurie, K. A., Fedorov, A. V. and Cherkaev, A. V.. Regularization of optimal design problems for bars and plates, Parts 1 and 2. J. Optim. Theory Appl. 37 (1982), 499521; 523–543.CrossRefGoogle Scholar
3Lurie, K. A. and Cherkaev, A. V.. Effective characteristics of composite materials and optimum design of constructive elements. Uspekhi Mekhaniki 9 (1986), 381 (in Russian).Google Scholar
4Cherkaev, A. V., Gibianskii, L. V. and Lurie, K. A.. Optimum focusing of heat flux by means of a non-homogeneous heat-conducting medium (DCAMM Report No. 305, The Technical University of Denmark, July 1985).Google Scholar
5Ball, J. M.. Convexity conditions and existence theorems in non-linear elasticity. Arch. Rational Mech. Anal. 63 (1977), 337407.CrossRefGoogle Scholar
6Strang, G.. The polyconvexification of F(∇u) (Research Report CMA-R09–83, The Australian National University, 1983).Google Scholar
7Rockafellar, R. T.. Convex Analysis (Princeton: Princeton University Press, 1970).CrossRefGoogle Scholar
8Dacorogna, B.. Weak Continuity and Weak Lower Semi-continuity for Non-linear Functional, Lecture Notes in Mathematics 922 (Berlin: Springer, 1982).CrossRefGoogle Scholar
9Goodman, J., Kohn, R. V. and Reyna, L.. Numerical study of a relaxed variational problem from optimal design. Comput. Methods Appl. Engrg. 57 (1986), 107127.CrossRefGoogle Scholar