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Mathematics > Optimization and Control

arXiv:1812.00289 (math)
[Submitted on 1 Dec 2018]

Title:On Bi-Objective convex-quadratic problems

Authors:Cheikh Toure, Anne Auger, Dimo Brockhoff, Nikolaus Hansen
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Abstract:In this paper we analyze theoretical properties of bi-objective convex-quadratic problems. We give a complete description of their Pareto set and prove the convexity of their Pareto front. We show that the Pareto set is a line segment when both Hessian matrices are proportional. We then propose a novel set of convex-quadratic test problems, describe their theoretical properties and the algorithm abilities required by those test problems. This includes in particular testing the sensitivity with respect to separability, ill-conditioned problems, rotational invariance, and whether the Pareto set is aligned with the coordinate axis.
Comments: 12 pages
Subjects: Optimization and Control (math.OC); Neural and Evolutionary Computing (cs.NE)
Cite as: arXiv:1812.00289 [math.OC]
  (or arXiv:1812.00289v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1812.00289

Submission history

From: Cheikh Toure [view email]
[v1] Sat, 1 Dec 2018 23:32:43 UTC (694 KB)
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