Contrasting Two Transformation-based Methods for Obtaining Absolute Extrema

Abstract In this note, we contrast two transformation-based methods to deduce absolute extrema and the corresponding extremizers. Unlike variation-based methods, the transformation-based methods of Carlson and Leitmann and the recent one of Silva and Torres are direct in that they permit obtaining solutions by inspection.

[1]  Dean A. Carlson Fields of Extremals and Sufficient Conditions for a Class of Variational Games , 2009 .

[2]  George Leitmann,et al.  A note on absolute extrema of certain integrals , 1967 .

[3]  George Leitmann,et al.  A Direct Method for Open-Loop Dynamic Games for Affine Control Systems , 2005 .

[4]  Quasi-Invariant Optimal Control Problems , 2003, math/0302264.

[5]  D. A. Carlson An Observation on Two Methods of Obtaining Solutions to Variational Problems , 2002 .

[6]  Fields of Extremals and Sufficient Conditions for the Simplest Problem of the Calculus of Variations in n-Variables , 2009 .

[7]  George Leitmann,et al.  Coordinate Transformation Method for the Extremization of Multiple Integrals , 2005 .

[8]  Delfim F. M. Torres,et al.  Absolute Extrema of Invariant Optimal Control Problems , 2006 .

[9]  A Noether Theorem on Unimprovable Conservation Laws for Vector-Valued Optimization Problems in Control Theory , 2004, math/0411173.

[10]  Delfim F. M. Torres,et al.  Automatic Computation of Conservation Laws in the Calculus of Variations and Optimal Control , 2005 .

[11]  Delfim F. M. Torres,et al.  Symbolic computation of variational symmetries in optimal control , 2006 .

[12]  Pierre Cartigny,et al.  An Extension of Leitmann's Direct Method to inequality Constraints , 2004, IGTR.

[13]  George Leitmann,et al.  Fields of extremals and sufficient conditions for the simplest problem of the calculus of variations , 2008, J. Glob. Optim..

[14]  George Leitmann,et al.  Some Extensions to a Direct Optimization Method , 2001 .