Leitmann’s direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales

2010/01/09 by Agnieszka B. Malinowska, Delfim F. M. Torres · 5 citations
Engineering · Mathematics · Medicine · #Applied mathematics #Calculus (dental) #Differential Equations and Boundary Problems #Elasticity and Wave Propagation #Mathematical analysis #Mathematical optimization #Mathematics #Maxima and minima #Medicine #Numerical methods for differential equations #Orthodontics #math.OC #msc:39A12 #msc:49J05 #msc:49M30

paper · pdf · doi:10.1016/j.amc.2010.01.015

published as Appl. Math. Comput. 217 (2010), no. 3, 1158--1162 · Accepted for publication (9/January/2010) in Applied Mathematics and Computation

arxiv created 2010/01/09 · openalex publication_date 2010/01/19 · arxiv updated 2010/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The fundamental problem of the calculus of variations on time scales concerns the minimization of a delta-integral over all trajectories satisfying given boundary conditions. This includes the discrete-time, the quantum, and the continuous/classical calculus of variations as particular cases. In this note we follow Leitmann's direct method to give explicit solutions for some concrete optimal control problems on an arbitrary time scale.

Citations

• Contrasting Two Transformation-based Methods for Obtaining Absolute Extrema
• Noether's theorem on time scales

Cited by

• A general backwards calculus of variations via duality
• Fractional Noether’s theorem in the Riesz–Caputo sense
• Fractional Calculus on Time Scales
• Generalizing the variational theory on time scales to include the delta indefinite integral
• Delta-nabla optimal control problems

Related

• Necessary optimality conditions for the calculus of variations on time scales
• On Optimality Conditions in Control Theory
• Variational Optimal-Control Problems with Delayed Arguments on Time Scales
• Fractional Calculus on Time Scales
• A Brief Survey of the History of the Calculus of Variations and its Applications