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A duality principle for non-convex optimisation and the calculus of variations. (English) Zbl 0411.49012


MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
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[1] Coffman, C. V., ”On variational principles for sublinear boundary value problems”, Jour. Diff. Eqns., 17 46–60 (1975). · Zbl 0292.49005
[2] Ekeland, I., & Temam, R., ”Analyse convexe et problemes variationeis”, Dunod, Gauthiers. Paris 1974. (English translation ”Convex analysis and variational problems”, North-Holland, Amsterdam 1976.) · Zbl 0281.49001
[3] Fenchel, W., ”Convex cones, sets and functions”, Notes de Cours polycopiees, Princeton University, 1951. · Zbl 0053.12203
[4] Kolodner, I.I., ”Heavy rotating string –a non-linear eigenvalue problem”, Comm. Pure Appl. Math., VIII 395–408 (1955). · Zbl 0065.17202
[5] Rockafellar, T.R., ”Duality and stability in extremal problems involving convex functions”, Pac. Jour. Math., 21, 167–187 (1967). · Zbl 0154.44902
[6] Rockafellar, T.R., ”Convex Analysis”, Princeton University Press, 1970. · Zbl 0193.18401
[7] Rockafellar, T.R., ”Convex integral functions and duality”, in Contributions to Nonlinear Functional Analysis (E. Zarantonello, ed.), Academic Press, 1971. · Zbl 0295.49006
[8] Rockafellar, T.R., ”Conjugate convex functions in optimal control and the calculus of variations”, Jour. Math. Anal. Appl., 32, 174–222 (1970). · Zbl 0218.49004
[9] Toland, J. F., ”On the stability of rotating heavy chains”, to appear, Jour. Diff. Eqns. · Zbl 0372.49016
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