Consider the following Bolza problem: min integral h(x, u)dt, x = F(x) + uG(x), \u\ less-than-or-equal-to 1, x is-an-element-of OMEGA subset-of R2, x(0) = x0, x(1) = x1. We show that, under suitable assumptions on F, G, h, all optimal trajectories are bang-bang. The proof relies on a geometrical approach that works for every smooth two-dimensional manifold. As a corollary, we obtain existence results for nonconvex optimization problems.

Bang-Bang Property for Bolza Problems in Two Dimensions / Crasta, Graziano; B., Piccoli. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - 83:1(1994), pp. 155-165. [10.1007/bf02191766]

Bang-Bang Property for Bolza Problems in Two Dimensions

CRASTA, Graziano;
1994

Abstract

Consider the following Bolza problem: min integral h(x, u)dt, x = F(x) + uG(x), \u\ less-than-or-equal-to 1, x is-an-element-of OMEGA subset-of R2, x(0) = x0, x(1) = x1. We show that, under suitable assumptions on F, G, h, all optimal trajectories are bang-bang. The proof relies on a geometrical approach that works for every smooth two-dimensional manifold. As a corollary, we obtain existence results for nonconvex optimization problems.
1994
01 Pubblicazione su rivista::01a Articolo in rivista
Bang-Bang Property for Bolza Problems in Two Dimensions / Crasta, Graziano; B., Piccoli. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - 83:1(1994), pp. 155-165. [10.1007/bf02191766]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/67146
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