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pith:XY7FWYDT

pith:2026:XY7FWYDTA3NTSPUEET5FLVY5QY

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Adaptive Metrics for Norm-Minimization-Based Outer Approximation in Convex Vector Optimization

Mohammed Alshahrani

Adaptive metrics extend improved convergence rates to all inner-product norms in convex vector optimization outer approximation.

arxiv:2605.14320 v1 · 2026-05-14 · math.OC · cs.NA · math.NA

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Claims

C1strongest claim

We prove that the improved Euclidean convergence rate O(k^{2/(1-q)}) extends to all fixed inner-product norms and establish a dispersion theorem showing that the cut normals generated by the algorithm naturally spread across all directions when the upper image has a strictly convex boundary with bounded curvature.

C2weakest assumption

The upper image has a strictly convex boundary with bounded curvature, which is required to guarantee that the adaptive metric remains well-conditioned throughout execution.

C3one line summary

An adaptive metric framework for outer approximation in convex vector optimization extends convergence rates to inner-product norms, proves a dispersion theorem under strict convexity, and achieves 31-33% fewer iterations than fixed Euclidean norm on curved Pareto fronts.

References

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[1] Q. H. Ansari, E. K¨ obis, and J.-C. Yao,Vector Variational Inequalities and Vector Optimization(Vector Optimization), en. Cham: Springer International Publishing, 2018.doi:10.1007/978-3-319-63049-6 2018 · doi:10.1007/978-3-319-63049-6

[2] A Norm Minimization-Based Convex Vector Optimization Algorithm, 2022

[3] Outer Approximation Algorithms for Convex Vector Optimization Problems, 2023

[4] Convergence Analysis of a Norm Minimization-Based Convex Vector Optimization Algorithm, 2024 · doi:10.1137/23m1574580

[5] A Class of Adaptive Algorithms for Approximating Convex Bodies by Polyhedra, 1992

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Cited by

1 paper in Pith

Convergence Rates for $\ell_p$ Norm Minimization in Convex Vector Optimization

Receipt and verification

First computed	2026-05-17T23:39:09.849277Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be3e5b607306db393e8424fa55d71d8619a280c537f4ff124670acd1a833b5ac

Aliases

arxiv: 2605.14320 · arxiv_version: 2605.14320v1 · doi: 10.48550/arxiv.2605.14320 · pith_short_12: XY7FWYDTA3NT · pith_short_16: XY7FWYDTA3NTSPUE · pith_short_8: XY7FWYDT

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/XY7FWYDTA3NTSPUEET5FLVY5QY \
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# expect: be3e5b607306db393e8424fa55d71d8619a280c537f4ff124670acd1a833b5ac

Canonical record JSON

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    "submitted_at": "2026-05-14T03:32:59Z",
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