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Optimization problems with convex epigraphs. Application to optimal control

Kryazhimskii A. V.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 4

773-801

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.