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arXiv · 2610.38553

Optimality Conditions and Solution Set Characterisations of Convex Minimal Time Optimisation Problems

Doan Huu Hieu·Nguyen Duy Cuong
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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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Doan Huu Hieu, Nguyen Duy Cuong. 2026-10-28. Optimality Conditions and Solution Set Characterisations of Convex Minimal Time Optimisation Problems. https://arxiv.org/abs/2610.38553

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