A bundle-filter method for nonsmooth convex constrained - download pdf or read online

By Elizabeth Karas, Ademir Ribeiro, Claudia Sagastizabal

For fixing nonsmooth convex restricted optimization difficulties, we advise an set of rules which mixes the guidelines of the proximal package tools with the filter out technique for comparing candidate issues. The ensuing set of rules inherits a few beautiful positive aspects from either ways. at the one hand, it permits powerful keep watch over of the scale of quadratic programming subproblems through the compression and aggregation options of proximal package deal tools. however, the filter out criterion for accepting a candidate element because the new iterate is usually more straightforward to fulfill than the standard descent situation in package deal tools. a few encouraging initial computational effects also are pronounced.

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Additional info for A bundle-filter method for nonsmooth convex constrained optimization

Example text

1 co~ue pr@c@demment. CHAPITRE V EXISTENCE DE V01SINAGES TUBULAIRES Dams ce chapitre, nous montrons que la construction ~e voisinages tubulaires d'une sous-vari@t@ d'une vari@t6 donn@e faite dams [ I~ (Chapitre IV) peut se parti- culariser au eas des structures @tal6es. ,,I,,,,~PR0~AGAT~URS ETALES (Layer-spray) Dgfinition I. Soit M une vari6t@ @tal6e model6e sur est une section du fibr6 double tangent br6 tangent sur (~,T,T',T") M v@rifiant les propri6t6s (iii) U~ T2M & la vari6t6 ~(~,KT) M (i) (i±), (iii).

Pi(I) = (1,1 ..... I .... ) Pi(I) quel que soit est situ6 dans est situ4 dans t < I , il existe un voisinage E° - E It de t dans [0,1] tel que 43 P1(It) soit contenu dans un espace de dimension finie. pi(t) = (~i(t), , IPl(t)lo 2 ,< Soit ~ rune 2t~(t 2) ..... Z n>/ I 9 ntn-1~(t n) .... ) ~? ant l'application <_ 0 nous renvoyons h [11]) ~r [ 2] et . > r Posons f(x) = = + p1(~r(l~ Io)) Nous remarquons que : a) f est une application E ~ E 0 b)~est do classe co C , en dehors de 0 . 0 l'identit6 en dehors de E (r) 0 s) f( i(E)- {o})ci(E) d) La restriction & E - {0} de f est une L(IdE) application.

DIFFE0~0RPHISME DE BESSAGA Th@or&me I. Soit E(z) la boule de centre morphisme de classe et tel que C°° , 0 et de rayon ~ : E - 101 ~ E r de E • I1 existe un diff@o- qui est l'identit@ en dehors de (~ - id) soit localement contenu dans un e s ~ c e de dimension finie. D@monstration. Un point de E(r) E, x ~est repr@sent@ par une suite de nombre r@els 42 x = {x 1 . . . xn .... Z ) ; n£1g Soit g tun n o m b r e > 0 x 2 <~}. n qui sera choisi ult6rieurement ~Xn 2 soit E = ix, ~=(x 1 ..... x n ....

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A bundle-filter method for nonsmooth convex constrained optimization by Elizabeth Karas, Ademir Ribeiro, Claudia Sagastizabal


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