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weft

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3Â¥: Originally posted by seu_adonis at 2013-08-06 09:30:03
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4Â¥: Originally posted by weft at 2013-08-06 13:33:37
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seu_adonis: ½ð±Ò+18, ¡ï¡ï¡ïºÜÓаïÖú 2013-08-08 09:51:05
Â¥Ö÷ºÍWeftµÄÌÖÂÛ´Ó¼¸ºÎ, Ìݶȷ½ÏòÌÖÂ۵ĺÜÉî¿ÌÁË,ÎÒ´Ó±í´ïʽ·½Ãæ»­ÉßÌí×ãÒ»ÏÂ.

Ê×ÏÈ, ·ûºÅ˵Ã÷.  w=(w1, w2,..., wN) ÊǸö¹Ì¶¨ÏòÁ¿ (²»ÐèÒª¼ÙÉè·ÖÁ¿wi>0).  
³¬Á¢·½Ìå{(x1,...,xN) | |xi|<=1} ¼ÇΪC,  ¼ÇÏòÁ¿ÄÚ»ýΪw. x   .  ÄÇô¦¸1 ={ x in C| w.x > b-a}, ÁíÍâÁ½¸ö·Ö±ðΪw.x  >  -b-a  ºÍ  w.x > -a. ÏÔÈ»¦¸1 °üº¬ÓÚ¦¸3°üº¬ÓÚ¦¸2ÖÐ.   

ÁíÍâ, ¼ÇP(k) ={ y in C| w.y =k}.  ÄÇô P(b-a) Æ½Ãæ¼ÐÔÚ P(-b-a) ºÍ P(b+a)Ö®¼ä. ÎÒÃÇÏÈÀ´¿´Ò»¸öÒýÀí:
ÒýÀí: P(b-a) µÄÃæ»ý ´óÓÚµÈÓÚ P(-b-a)=P(b+a), ¶ÔÓÚÈÎÒâʹµÃP(a+b)>0µÄa>0, b>0.
Ö¤Ã÷: Ö»²»¹ýÖØ¸´Â¥Ö÷¹ØÓÚÌݶȵÄ˼·,Ö»ÊDZí´ï·½Ê½²»Í¬.
²»·ÁÉèP(b-a), P(b+a) ¶¼ÔÚP(0) µÄͬһ²à, ¼´ (b>a).
ÏÔÈ»P(b+a)ÊÇ͹ÐÎ, ÈÎÒâȡһ¸ö¼«Öµµãy0 (Extreme point). ÔòÁ½¸ö¼¯ºÏ{ 1/2 * (y-y0) : y \in P(a+b)}
ºÍ{ 1/2 * (y0 -y) : y \in P(a+b) } Ö»ÏཻÓÚÔ­µã, Ò²¾ÍÊÇy=y0µÄʱºò. ͬʱ, ÕâÁ½¸ö¼¯ºÏ¶¼»¹ÔÚCÄÚ,ÒòΪCÊǹØÓÚÔ­µãÖÐÐĶԳƵÄ͹¼¯. ÄÇô, ÎÒÃÇ¿´³öÈçÏÂÁ½¸ö¼¯ºÏ
(¼ÓȨƽ¾ùµÃµ½)
{ (b-a)/(b+a)*y + 2a/(b+a)* 1/2 * (y-y0) : y \in P(a+b) } ºÍ{ (b-a)/(b+a)*y0 + 2a/(b+a)* 1/2 * (y0-y) : y \in P(a+b) } ÊÇ (1) Ö»ÏཻÓÚÒ»µã;  (2) ÔÚCÄÚ; (3)ÊôÓÚP(b-a).
ÓÉÓÚÕâÁ½¸öP(b-a)µÄ×Ó¼¯¶¼Ö»ÊÇP(a+b)µÄÏßÐԱ任, Ãæ»ýÒ²ÊdzËÒÔÒ»¸öÏßÐÔÒò×Ó,ËùÒÔ
P(b-a) >= b/(b+a)* P(a+b) + a/(b+a)* P(a+b) = P(a+b). ÒýÀíµÃÖ¤.

ÏÖÔڻص½Ô­Ìâ.  ÒªÖ¤Ã÷£º|¦¸1|+|¦¸2|<2*|¦¸3|£¬Ö»ÐèÒªÖ¤Ã÷ | ¦¸3 - ¦¸1| > | ¦¸2 - ¦¸3| ¼´¿É.  |¦¸|(±íʾ¿Õ¼ä¦¸µÄ´óС)¿ÉÒÔÓÉ»ý·Ö¸ø³ö, ÆäÖÐ, »ý·ÖԪΪw·½ÏòµÄһάֱÏßdx, ´ÓÁãµ½b, »ý·Öº¯Êý·Ö±ðΪP(x-a) (¶ÔÓÚ¦¸3 - ¦¸1) ºÍP(-x-a)(¶ÔÓÚ¦¸2 - ¦¸3)µÄÃæ»ý.  ÒýÀí¸æËßÎÒÃÇP(-x-a) <= P(x-a), ÄÇ×ÔÈ»»ý·Ö¾Í| ¦¸2 - ¦¸3|<=| ¦¸3 - ¦¸1| ÁË.

»¹ÓÐ, ÎҺܱ§Ç¸,Ö»ÄÜÖ¤Ã÷ СÓÚµÈÓÚ, »¹²»ÊÇÂ¥Ö÷ÒªÇóµÄÑϸñСÓÚºÅ.
We_must_know. We_will_know.
6Â¥2013-08-08 01:23:35
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seu_adonis

гæ (³õÈëÎÄ̳)

ÒýÓûØÌû:
6Â¥: Originally posted by hank612 at 2013-08-08 01:23:35
Â¥Ö÷ºÍWeftµÄÌÖÂÛ´Ó¼¸ºÎ, Ìݶȷ½ÏòÌÖÂ۵ĺÜÉî¿ÌÁË,ÎÒ´Ó±í´ïʽ·½Ãæ»­ÉßÌí×ãÒ»ÏÂ.

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