TL;DR
Determining whether a convex function is self-concordant is computationally intractable, as proven by an elementary proof showing NP-hardness, highlighting limitations in verifying this property efficiently.
Contribution
The paper provides an elementary proof that deciding self-concordance of convex functions is NP-hard, establishing computational complexity results for this property.
Findings
Deciding self-concordance is NP-hard.
Elementary proof of intractability.
Implications for optimization and convex analysis.
Abstract
We give an elementary proof of a somewhat curious result, namely, that deciding whether a convex function is self-concordant is in general an intractable problem.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Advanced Algebra and Logic · Advanced Optimization Algorithms Research