Examples of ill-behaved central paths in convex optimization

Jean Charles Gilbert (1) , Clóvis C. Gonzaga , Elizabeth Karas

1 ESTIME - Parameter estimation and modeling in heterogeneous media

This paper presents some examples of ill-behaved central paths in convex optimization. Some contain infinitely many fixed length central segments; others manifest oscillations with infinite variation. These central paths can be encountered even for infinitely differentiable data.

Mots clés: CENTRAL PATH; CONVEX OPTIMIZATION; INTERIOR POINT ALGORITHM; NONLINEAR PROGRAMMING; PENALTY FUNCTION METHODS

Domaines: Mathématiques [math]

Jean Charles Gilbert, Clóvis C. Gonzaga, Elizabeth Karas. Examples of ill-behaved central paths in convex optimization. Mathematical Programming, 2005, 103, pp.63-94. ⟨10.1007/s10107-003-0460-0⟩. ⟨inria-00072443⟩