Geodesic
Optimization problems with convex epigraphs. Application to optimal control
International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) no. 4, pp. 773-801

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For a class of infinite-dimensional minimization problems with nonlinear equality constraints, an iterative algorithm for finding global solutions is suggested. A key assumption is the convexity of the "epigraph", a set in the product of the image spaces of the constraint and objective functions. A convexification method involving randomization is used. The algorithm is based on the extremal shift control principle due to N.N. Krasovskii. An application to a problem of optimal control for a bilinear control system is described.
Keywords: nonconvex optimization, global optimization methods
Mots-clés : równanie nieliniowe, optymalizacja 
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     author = {Kryazhimskii, A. V.},
     title = {Optimization problems with convex epigraphs. {Application} to optimal control},
     journal = {International Journal of Applied Mathematics and Computer Science},
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     number = {4},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2001_11_4_a1/}
}
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Kryazhimskii, A. V. Optimization problems with convex epigraphs. Application to optimal control. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) no. 4, pp. 773-801. http://geodesic.mathdoc.fr/item/IJAMCS_2001_11_4_a1/