Optimality Conditions and Solution Set Characterisations of Convex Minimal Time Optimisation Problems
Abstract
The paper studies convex minimisation problems involving a composition of a coordinatewise nondecreasing convex function with a finite family of nonnegative, locally Lipschitz continuous and convex functions. We establish complete dual optimality conditions and characterise the entire solution set using multipliers and subgradients associated with a given solution. The results are applied to norm optimisation problems involving minimal time functions with different convex dynamics sets and convex target sets. The sum, maximum and p-norms yield minimal time versions of the Fermat--Torricelli, Chebyshev centre and p-Fermat--Torricelli problems, respectively. Examples in finite and infinite dimensional spaces are provided to illustrate the solution set characterisations.
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BibTeX
@misc{hieu2026optimality,
title = {{Optimality Conditions and Solution Set Characterisations of Convex Minimal Time Optimisation Problems}},
author = {Doan Huu Hieu and Nguyen Duy Cuong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38553},
eprint = {2610.38553},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38553},
}
RIS
TY - UNPB
TI - Optimality Conditions and Solution Set Characterisations of Convex Minimal Time Optimisation Problems
AU - Doan Huu Hieu
AU - Nguyen Duy Cuong
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38553
UR - https://arxiv.org/abs/2610.38553
AB - The paper studies convex minimisation problems involving a composition of a coordinatewise nondecreasing convex function with a finite family of nonnegative, locally Lipschitz continuous and convex functions. We establish complete dual optimality conditions and characterise the entire solution set using multipliers and subgradients associated with a given solution. The results are applied to norm optimisation problems involving minimal time functions with different convex dynamics sets and convex target sets. The sum, maximum and p-norms yield minimal time versions of the Fermat--Torricelli, Chebyshev centre and p-Fermat--Torricelli problems, respectively. Examples in finite and infinite dimensional spaces are provided to illustrate the solution set characterisations.
ER -