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 ones of Carlson and Leitmann and the recent one of Silva and Torres are direct in that they permit obtaining solutions by inspection.

9 pages

References in corpus (2)

• Automatic Computation of Conservation Laws in the Calculus of Variations and Optimal Control
• A Noether Theorem on Unimprovable Conservation Laws for Vector-Valued Optimization Problems in Control Theory

Cited by in corpus (8)

• Discrete-Time Fractional Variational Problems
• Fractional Noether's theorem in the Riesz-Caputo sense
• The Hahn Quantum Variational Calculus
• Leitmann's direct method for fractional optimization problems
• Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales
• Fractional Euler-Lagrange differential equations via Caputo derivatives
• Towards a combined fractional mechanics and quantization
• Hahn's Symmetric Quantum Variational Calculus