The necessity of differentiability in componentwise optimization — A remark on a theorem of Oettli

Short communication The necessity of differentiability in componentwise optimization- A remark on a theorem of Oettli K.l~i. MJELDE

has the objective value 3. I. Componentwise optimi. ~ttion shows that .~ is repeated int'mitely in the algorithm of Oettli, since xl = ( I, O) is optimal with Jr2 = (0, !)given, and conversely. However, the opttmal solution is:

SIIAPE TechnicalCentre, The Hague.NetherMnds ReceivedNovemberI978 Revisedjanuary 1979

~..kttli {l] proved that the maximum of a concave and differentiabte function with each variable occurring in a sLng!ecomponent-constzaint can 0e determined ~y ¢omponentwis¢ optimization. The fact ~hat diflerentiability is a necessary assumption is demonstrated by the following examl:te (or' +he allocation of 2 re~urces to 2 activities).

with objective value !~.

Acknowledgement A referee improved the con¢isen(ss of presentation.

Example max[mia(3,3xtt + 2x21) + 2xt2 ÷ 0.1x22] ,

Reference

s.t.xil÷xl~=l xq~O

[ I [ W.Oetl|m,Einzelschfirtverfahrenzur LOsungkonvexer

fori= 1,2; for/--l,2

and/= 1,2.

und dual-konvexerMinimi~rung~probleme,ZAMM 54

(1974"1343-351.

The feasible solution J given by:

O North-Ilolland PublishingCompany European Journal of OpezationalReseaxch3 (1979) 340,

340