Explicit bounds for Lipschitz constant of solution to basic problem in calculus of variations

2017/12/13 by Miguel Oliveira, Oliveira, Miguel, Georgi Smirnov +1
Computer Science · Decision Sciences · Mathematics · #49J24 #49M15 #49M37 #49N60 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.1712.04825

openalex publication_date 2017/12/13 · openalex created_date 2017/12/22 · openalex updated_date 2026/07/28

Abstract

In this paper we present explicit estimate for Lipschitz constant of solution to a problem of calculus of variations. The approach we use is due to Gamkrelidze and is based on the equivalence of the problem of calculus of variations and a time-optimal control problem. The obtained estimate is used to compute complexity bounds for a path-following method applied to a convex problem of calculus of variations with polyhedral end-point constraints.

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