Examples of Ill-Behaved Central Paths in Convex Optimization

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Submitted on 24 May 2006

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Examples of Ill-Behaved Central Paths in Convex Optimization

Jean Charles Gilbert, Clóvis C. Gonzaga, Elizabeth Karas

To cite this version:

Jean Charles Gilbert, Clóvis C. Gonzaga, Elizabeth Karas. Examples of Ill-Behaved Central Paths in

Convex Optimization. [Research Report] RR-4179, INRIA. 2001. �inria-00072443�

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ISRN INRIA/RR--4179--FR

a p p o r t

d e r e c h e r c h e

THÈME 4

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Examples of ill-behaved central paths in convex optimization

Jean Charles — Clóvis C.

— Elizabeth

N° 4179

3 mai 2001

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Examples of Ill-Behaved Central Paths in Convex Optimization

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https://hal.inria.fr/inria-00072443

Submitted on 24 May 2006

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Examples of Ill-Behaved Central Paths in Convex Optimization

Jean Charles Gilbert, Clóvis C. Gonzaga, Elizabeth Karas

To cite this version:

Jean Charles Gilbert, Clóvis C. Gonzaga, Elizabeth Karas. Examples of Ill-Behaved Central Paths in

Convex Optimization. [Research Report] RR-4179, INRIA. 2001. �inria-00072443�

ISRN INRIA/RR--4179--FR

a p p o r t

d e r e c h e r c h e

THÈME 4

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Examples of ill-behaved central paths in convex optimization

Jean Charles — Clóvis C.

— Elizabeth

N° 4179

3 mai 2001

y=0

0 y=0

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y k−1

b k−1

b k +a

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r k

f k

f k−1

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0.2 0.4 0.6 0.8 1 1.2 1.4

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0.2 0.4 0.6 0.8 1 1.2 1.4

0

ϕ

f 1

f 2 f

0

−1 0 1 2 0

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Density function

−1 0 1 2

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Second integral

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Smoothing function

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2

0 0.5 1 1.5

f ₂ f