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Self-concordant function

A self-concordant function is a function satisfying a certain differential inequality, which makes it particularly easy for optimization using Newton's method: Sub.6.2.4.2 A self-concordant barrier is a particular self-concordant function, that is also a barrier function for a particular convex set. Self-concordant barriers are important ingredients in…

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Self-concordant barriers

Cartesian productSlater's conditionQuadratic functionsProduct ruleEpigraph
15 related topics

History

Yurii NesterovArkadi NemirovskiLipschitz continuousAffine transformation
4 related topics

Self-concordant functions

Open setFunction
2 related topics

Properties

Convex conjugate
1 related topics

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Overview

Self-concordant functions

Self-concordant barriers

History

Properties

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Self-concordant function

Nodes33
Edges32
Triples30
Avg. degree1.94
Density0.060606
Components1

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Self-concordant function

Top relations

related to history · 10
Self-concordant function → Arkadi Nemirovski, As, Ay, Bibliography Comments, Hessian, However, If, Lipschitz, Newton, Yurii Nesterov
has application · 6
Self-concordant function → Among, Lipschitz, Newton, Newton's, Self-concordant, The
related to Basic SCBs · 6
Self-concordant function → Every, For, It, Note, Rn, This
related to Multivariate self-concordant function · 4
Self-concordant function → Here, Let, Rn, We
related to Minimizing a self-concordant function · 3
Self-concordant function → Hessian, Newton, We
is a · 1
Self-concordant function → function satisfying a certain differential inequality

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Important terminology

displaystyle function self-concordant leq barrier mathbb convex domain ln functions also parameter linear rn defined geq interior rule -x using

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Self-concordant functionis afunction satisfying a certain differential inequality0.90text
Self-concordant functionhas applicationAmong0.60section
Self-concordant functionhas applicationNewton's0.60section
Self-concordant functionhas applicationSelf-concordant0.60section
Self-concordant functionhas applicationThe0.60section
Self-concordant functionhas applicationNewton0.60section
Self-concordant functionhas applicationLipschitz0.60section
Self-concordant functionrelated to Basic SCBsEvery0.60section
Self-concordant functionrelated to Basic SCBsRn0.60section
Self-concordant functionrelated to Basic SCBsIt0.60section
Self-concordant functionrelated to Basic SCBsNote0.60section
Self-concordant functionrelated to Basic SCBsFor0.60section

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