IMA Journal of Mathematical Control and Information - Advance Access http://imamci.oxfordjournals.org IMA Journal of Mathematical Control and Information - RSS feed of articles 1471-6887 IMA Journal of Mathematical Control and Information 0265-0754 <![CDATA[Sufficiency by a direct method in the variable state problem of calculus of variations: singular extremals]]> http://imamci.oxfordjournals.org/cgi/content/short/dnp009v1?rss=1 A direct sufficiency proof for singular and non-singular extremals for the parametric variable state problem of Bolza in the calculus of variations is presented. This technique is self-contained in the sense that it makes no use of the classical concepts of conjugate or focal points, fields of extremals or certain matrix Riccati inequalities. Moreover, we also study the non-parametric variable state problem of Bolza and derive sufficient conditions for singular and non-singular extremals for weak and strong local minima.

]]> 2009-06-08 info:doi/10.1093/imamci/dnp009 Institute of Mathematics and its Applications 2009-06-08 Article