Summary: Äèôôåðåíöèàëüíûå óðàâíåíèÿ, ò. 31, No.11, 1995, ñ. 17861795.
ÓÄÊ 517.977
À.Ñ. ÀÍÒÈÏÈÍ
Î ÄÈÔÔÅÐÅÍÖÈÀËÜÍÛÕ ÃÐÀÄÈÅÍÒÍÛÕ ÌÅÒÎÄÀÕ
ÏÐÎÃÍÎÇÍÎÃÎ ÒÈÏÀ ÄËß ÂÛ×ÈÑËÅÍÈß ÍÅÏÎÄÂÈÆÍÛÕ
ÒÎ×ÅÊ ÝÊÑÒÐÅÌÀËÜÍÛÕ ÎÒÎÁÐÀÆÅÍÈÉ 1
(Ïåðåñìîòðåíî 1 äåêàáðÿ 2003)
1. Ïîñòàíîâêà ïðîáëåìû. Ðàññìîòðèì çàäà÷ó âû÷èñëåíèÿ íåïîäâèæíîé òî÷êè
ýêñòðåìàëüíîãî îòîáðàæåíèÿ
v # # Argmin{#(v # , w) | w
## }, v #
## # , (1.1)
ãäå ôóíêöèÿ #(v, w) îïðåäåëåíà íà ïðîèçâåäåíèè ïðîñòðàíñòâ R n
× R n
è# # R n .
Ïðåäïîëàãàåòñÿ, ÷òî #(v, w) âûïóêëàÿ ïî ïåðåìåííîé w
## ïðè êàæäîì ôèêñèðî-
âàííîì v
## , ýêñòðåìàëüíîå (ìàðãèíàëüíîå) îòîáðàæåíèå G(v) # argmin{#(v, w) |
| w

Source: Antipin, Anatoly S. - Dorodnicyn Computing Centre of the Russian Academy of Sciences

Collections: Computer Technologies and Information Sciences; Mathematics