不動点理論と最適化

演習の解説および総括
明治⼤学理⼯学部情報科学科
飯塚秀明
連続最適化および関連分野に関する
夏季学校
2021年8⽉23⽇, 24⽇© Meiji University,All rights reserved.

演習（数学とプログラミングの問題）

q演習（PDF参照下さい）
m8/23 16:35ー17:05
m8/24 10:00ー10:30

q発表・解説および総括
m8/24 10:40ー11:40© Meiji University,All rights reserved.

1. (ii)
2乗ノルム展開<latexit sha1_base64="COVlAXDBwiluNPF3+rs35ajgwK4=">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</latexit>22

kx + yk = kxk + 2hx, yi + kyk

2

Cauchy-Schwarz

 kxk2 + 2kxkkyk + kyk2
<latexit sha1_base64="ucQ54anHzfEzXmpYWyZrLLBgH5o=">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</latexit>= (kxk + kyk)2<latexit sha1_base64="v2T6iZuqHc4bKdArRjvemrRVZOM=">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</latexit>© Meiji University,All rights reserved.

1. (v)<latexit sha1_base64="5zf+cGnHP0oIY7NNdOumJUH0To4=">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</latexit>

`2 =

(

1
X

x = (xi ) : kxk2 =

i=1<latexit sha1_base64="4qQeyOqarBrNkO1Lie4TYnVjk50=">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</latexit>|xi |2 < 1

en = (0, 0, . . . , 0, 1, 0, 0, . . .) 2 `| {z })2n 1

hy, en i = yn
y = (y1 , y2 , . . .) 2 `2
1
1
1
X
X
X
1 > kyk2 =|yi |2 =|yn |2 =|hy, en i|2<latexit sha1_base64="9QTT9VmMRCyHyShBmLt3nPmLIC4=">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</latexit><latexit sha1_base64="ou/uB33AiLtGJk9F7s9XSOkjMKU=">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</latexit><latexit sha1_base64="Xudo1kbzjcbLFbrHZrKCWGGjSls=">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</latexit>

i=1) lim |hy, en i|2 = 0<latexit sha1_base64="pTjNkJV+mmvFz8KqVMtNU2pdNfA=">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</latexit>

n!1© Meiji University,All rights reserved.

n=1

n=1

1. (v)<latexit sha1_base64="5zf+cGnHP0oIY7NNdOumJUH0To4=">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</latexit>

`2 =

(

1
X

x = (xi ) : kxk2 =

i=1<latexit sha1_base64="4qQeyOqarBrNkO1Lie4TYnVjk50=">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</latexit>|xi |2 < 1

en = (0, 0, . . . , 0, 1, 0, 0, . . .) 2 `| {z }2n 1

y = (y1 , y2 , . . .) 2 `2<latexit sha1_base64="ou/uB33AiLtGJk9F7s9XSOkjMKU=">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</latexit>) lim |hy, en i| = 0<latexit sha1_base64="pTjNkJV+mmvFz8KqVMtNU2pdNfA=">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</latexit>2

hy, en i = yn<latexit sha1_base64="9QTT9VmMRCyHyShBmLt3nPmLIC4=">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</latexit>n!1) lim hy, en i = 0 = hy, 0i<latexit sha1_base64="MZ2wKlS5cEHfWRKIlFMSq3qqVYc=">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</latexit>n!1) en * 0<latexit sha1_base64="zTAdgea9d/4MapouiLT2rLHZ8Q8=">AAADfHicpVLNThRBEK7d8QfxhwUuJF4mrBgT46bWECCeiFw48uMCCUs2M2PtboeZ7klP7wJu9srBF/DgSRIORK/6Al58AQ88AuGIiRdjrO4dQ5SIJvZkpqq/rq+qv5oK01hkBvG4UPSuXL12fejG8M1bt++MlEbH1jLV0RHVIhUrvREGGcVCUs0IE9NGqilIwpjWw+0Fe77eJZ0JJZ+ZvZS2kqAlRVNEgWGoUfLrpk2amkqTTw3p17VotU070KlSspP62CiVsYJu+Redau6UIV9LarQwCXV4Dgoi6EACBBIM+zEEkPGzCVVASBnbgh5jmj3hzgn6MMzcDkcRRwSMbvO3xbvNHJW8tzkzx464SsyvZqYPU/gZj/AMP+FbPMFvf8zVcznsXfbYhgMupY2RlxOrX//KStgaaJ+zLmGEHH25JgNNmHNaBGtLHWJVRoP83RevzlafrEz17uMBnrK+N3iMH1mh7H6JDpdp5bXLLpmz47qRuPtJ7n+PcdvdlkN2OZ9FFNcgRq0G27ef/dzh+lZVzDZxfpb/nXN+/59qWR3/U2vA7/PcVX+fsovO2uNKdaYyvTxdnn+aT+AQ3IVJeMBTNgvzsAhLUOPb7sM7eA8fit+9e95D79EgtFjIOePwy/JmfgD/WMnJ</latexit>© Meiji University,All rights reserved.

)

1. (v)<latexit sha1_base64="5zf+cGnHP0oIY7NNdOumJUH0To4=">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</latexit>

`2 =

(

x = (xi ) : kxk2 =<latexit sha1_base64="4qQeyOqarBrNkO1Lie4TYnVjk50=">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</latexit>

1
X
i=1

|xi |2 < 1

en = (0, 0, . . . , 0, 1, 0, 0, . . .) 2 `| {z }
n 1

en * 0<latexit sha1_base64="a11HlJ4WE5PqGfpV9/SNULOMPDI=">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</latexit>

ken<latexit sha1_base64="a3sf+ngDJSwPgO5GvdKLyoA8jbY=">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</latexit>

0k = ken k = 1 6= 0

) en 9 0<latexit sha1_base64="jFGDGCzAGf71W84FSoSsqVlBeD0=">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</latexit>© Meiji University,All rights reserved.

2)1. (vi)>ei = (0, 0, . . . , 0, 1, 0, 0, . . . , 0) 2 R| {z }<latexit sha1_base64="dzZUnLxZy5Ue6NNhMTdofljB+hM=">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</latexit>i 1>

xn = (a1,n , a2,n , . . . , aN,n ) 2 R<latexit sha1_base64="roT91sqtgqBXHtV9tqNVijfwmvw=">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</latexit>

NN* x = (a1 , a2 , . . . , aN )> 2 RN
<latexit sha1_base64="D0G3SaCMTf3SgSxs6urgiqogEO0=">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</latexit><latexit sha1_base64="E4yr0pgU8UOA0Z7PgOwwF8aKFWE=">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</latexit>

8i,

0 = lim hxn
n!1<latexit sha1_base64="5+4BL3KRRBDdhneJg9PZYhhWF8E=">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</latexit>

x, ei i = lim (ai,n8i, lim ai,n = ai
n!1

© Meiji University,All rights reserved.

n!1

ai )

1. (vi)>ei = (0, 0, . . . , 0, 1, 0, 0, . . . , 0) 2 R| {z }<latexit sha1_base64="dzZUnLxZy5Ue6NNhMTdofljB+hM=">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</latexit>i 1>

xn = (a1,n , a2,n , . . . , aN,n ) 2 R<latexit sha1_base64="roT91sqtgqBXHtV9tqNVijfwmvw=">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</latexit>

NN* x = (a1 , a2 , . . . , aN )> 2 RN
<latexit sha1_base64="D0G3SaCMTf3SgSxs6urgiqogEO0=">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</latexit><latexit sha1_base64="5+4BL3KRRBDdhneJg9PZYhhWF8E=">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</latexit>

8i, lim ai,n = ai
n!1<latexit sha1_base64="oJVkesq1nFIMd3mChuzxjnj4TSk=">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</latexit>

kxn

2

xk =

© Meiji University,All rights reserved.

N
X
i=1

(ai,n

2

ai ) ! 02. (iii)

a 6= 0n
H = H(a, r) = {x 2 R : ha, xi  r}
⌧✓
◆ ✓
◆
a1
x1
= a1 x1 + a2 x2
r
,
a2
x2
<latexit sha1_base64="R86Zgx6hMtIPZ+YMcgKSvdUJpX0=">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</latexit><latexit sha1_base64="XnYSKj0MXa0Eoe84vJz9d+m68qY=">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</latexit><latexit sha1_base64="NZnA9z81BFRcyfNJ1UqQsOU3F5s=">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</latexit><latexit sha1_base64="c+MHMtGNOr29aIbyz4gN9yIK2cM=">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</latexit>a<latexit sha1_base64="5+VYIzj8nGz8F5HQJ6+OUf/h1lA=">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</latexit>© Meiji University,All rights reserved.

2. (iii)

a 6= 0n
H = H(a, r) = {x 2 R : ha, xi  r}<latexit sha1_base64="R86Zgx6hMtIPZ+YMcgKSvdUJpX0=">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</latexit><latexit sha1_base64="XnYSKj0MXa0Eoe84vJz9d+m68qY=">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</latexit><latexit sha1_base64="bLKxlFRj8gI/zv6EdP7gPPRM9qk=">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</latexit>

PH (x) = x+ ta
ha, PH (x)i = r<latexit sha1_base64="YqfE4n/FTTZ8Wd+Or88MbKhp2tE=">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</latexit><latexit sha1_base64="1UTOCIWgxxNCK03m9h5wfaPaJm8=">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</latexit>x<latexit sha1_base64="sq8GHmBriaGQnyLi6eP+MmAshvE=">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</latexit>a<latexit sha1_base64="cr/NOvMjcFfhxXOL0wZWvGb+HwM=">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</latexit>

ha, x + tai = r<latexit sha1_base64="mAwVyIiIbz8M0mAZPX+76aU5O2M=">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</latexit><latexit sha1_base64="5+VYIzj8nGz8F5HQJ6+OUf/h1lA=">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</latexit>

2<latexit sha1_base64="B+1h/1ZQJPYXAmtjliGSZ81uNWY=">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</latexit><latexit sha1_base64="wp3JiiuTeFy+ahdqs+NSgVuN/Lk=">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</latexit>

PH (x)

ha, xi + tkak = r
r ha, xit=
kak2
0<latexit sha1_base64="XVP6RDPcTrPdG0pFM2Au4GiDPi8=">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</latexit><latexit sha1_base64="kYcv5GfPwjPt0FRwvHbQHB8+0no=">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</latexit>© Meiji University,All rights reserved.

2. (iii)

a 6= 0n
H = H(a, r) = {x 2 R : ha, xi  r}(
r ha,xi
x + kak2 a (x 2
/ H),
PH (x) =x(x 2 H)<latexit sha1_base64="R86Zgx6hMtIPZ+YMcgKSvdUJpX0=">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</latexit><latexit sha1_base64="XnYSKj0MXa0Eoe84vJz9d+m68qY=">AAADu3icpVLNThRBEK5lVBB/WPRi4qXDBgOJ2fQagsaEhOBlj7C4QMLgpntslpaenrGnd/mZzAv4Ah48aeLB+BjGxBfwwCMYjmC8eLC6d5QoAU3syUxXfV1fVX81xVMlM0vpQWUouHDx0vDI5dErV69dH6uO31jJkp6JRDtKVGLWOMuEklq0rbRKrKVGsJgrscq3H7nz1b4wmUz0Y7uXio2YdbXclBGzCHWqnSaZI82pkMc5K+6aafTCnDh3tyCh1CSMmd3iPG8VT9BxBXFTTHeVICXrV7gpYSWeE0NwhUWnWqN16hc5bTRKowblWkzGKxMQwlNIIIIexCBAg0VbAYMMn3VoAIUUsQ3IETNoSX8uoIBR5PYwSmAEQ3Qbv1301ktUo+9yZp4dYRWFr0EmgUn6mb6jR/QTfU+/0O9n5sp9DneXPdz5gCvSztiLW8vf/sqKcbewdcI6h8Ex+nxNFjbhgdciUVvqEacyGuTv7788Wn7Ymszv0Df0EPW9pgf0AyrU/ePo7ZJovfLZNXJ2fDdifz+N/c8Rd93temQX8zkkwRoCUafB9e1nP3ewvlOlcI+9nZV/54Rf/FMtp+N/ag34bu4af07ZaWPlXr0xW59ZmqnNL5QTOAK3YQKmcMruwzw0YRHaeNuPcAjH8DWYC6LgWaAGoUOVknMTfltB7wfqxd+Z</latexit><latexit sha1_base64="HtKjR8tCxSyLVxrlTVzjav03ScA=">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</latexit>a<latexit sha1_base64="5+VYIzj8nGz8F5HQJ6+OUf/h1lA=">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</latexit><latexit sha1_base64="wp3JiiuTeFy+ahdqs+NSgVuN/Lk=">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</latexit>

PH (x)<latexit sha1_base64="XVP6RDPcTrPdG0pFM2Au4GiDPi8=">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</latexit>

0<latexit sha1_base64="kYcv5GfPwjPt0FRwvHbQHB8+0no=">AAADYHicpVI9TxtBEH32EeIQwDg0EWmQLSIqa4xQQKms0KTkIzaWbAvdXRZzcF+6O5s4J/+BVOmiJFUiUUT5GTT8AQradBGlkdJQMLs+ZCUWEIk93c3s23kz++bG8G0rjIjOUmlt7MH4w8yjiceTU9PZmdyTaui1A1NUTM/2gpqhh8K2XFGJrMgWNT8QumPYYts4WJPn2x0RhJbnvom6vmg6esu1di1TjxiqNgwnpt7OTIGKpNb8qFNKnAKSte7lUnk08BYeTLThQMBFxL4NHSE/dZRA8BlrImYsYM9S5wI9TDC3zVGCI3RGD/jb4l09QV3ey5yhYptcxeY3YOY8FuiUflCfTugn/abLG3PFKoe8S5etMeAKfyf74enWnztZDtsIe0PWLQyDo2/XFGEXq0qLxdp8hUiV5iB/5/2n/tbLzYX4OX2nc9b3jc7omBW6nQvzaENsflXZXeYcqm446n4u9z9mXHa3pZB3nE8iHtcQjEoNsm/X/Tzk+lKVzdZRfpj8nSG/91+1pI771Brw5dyV/p2yUae6VCy9KC5vLBfKr5IJzOAZ8ljkKVtBGa+xjgrfdh8f8Rlf0r+0jJbVcoPQdCrhzOKvpc1dAV1Mvq8=</latexit>© Meiji University,All rights reserved.

t=rha, xikak2

2. (vi)<latexit sha1_base64="zsuIA2942e42V6HWB7y0J+3GZUg=">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</latexit>

m
\

i=1

Ci 6= ;

T = P1 P2 · · · Pm
<latexit sha1_base64="GVa6SMAW4clbAX6jUp5vajJi1ZM=">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</latexit><latexit sha1_base64="WOTi0aj4J+Ew4wiNQ9g2jZzhtFU=">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</latexit>=) Fix(T ) ⇢m = 1 は明らか。
m = 2 のときに成り立つことを示しましょう。

© Meiji University,All rights reserved.

m
\

i=1

Ci

2. (vi)<latexit sha1_base64="Tz3jCxCyONN98g1EOV5XlI3mS90=">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</latexit>

Fix(P1 P2 ) ⇢ C1 \ C2 6= ;x 2 Fix(T )(= Fix(P1 P2 )P2 (x) 2 C1
① x2
② x 2 C2/ C2
P2 (x) 2/ C1<latexit sha1_base64="14TMkNW3mYqvhhU/1j4aRobhQsU=">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</latexit><latexit sha1_base64="vIPDOOcc8Q81YPYcb6x/lymFaRA=">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</latexit><latexit sha1_base64="pZSAEruWQrPq+14FOEuw0xGqztk=">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</latexit><latexit sha1_base64="TZUoVp4OEel7/7kDedjsj1oA8oc=">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</latexit>

すべてのパターン①, ②
に対して証明すればよい

C1<latexit sha1_base64="ZLf7mOqzUhWQ8OvR8rdXHwJtKxA=">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</latexit>© Meiji University,All rights reserved.

C2<latexit sha1_base64="cgtnFgmvq+yUCUFjoylqQOIiZMI=">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</latexit>2. (vi)<latexit sha1_base64="Tz3jCxCyONN98g1EOV5XlI3mS90=">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</latexit>

Fix(P1 P2 ) ⇢ C1 \ C2 6= ;x 2 Fix(T ) = Fix(P1 P2 )<latexit sha1_base64="14TMkNW3mYqvhhU/1j4aRobhQsU=">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</latexit>x2/ C2 ^P2 (x) 2/ C1 ？
<latexit sha1_base64="TZUoVp4OEel7/7kDedjsj1oA8oc=">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</latexit><latexit sha1_base64="+gSeempOnF69+EFnjf/p2Efok4E=">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</latexit><latexit sha1_base64="lGIF47dbP5vn4ITNolFZ7d5L7bs=">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</latexit>x<latexit sha1_base64="VNo29VfyYPdT4pnbfcVYwpRQew0=">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</latexit>

C1

P2 (x)<latexit sha1_base64="ZLf7mOqzUhWQ8OvR8rdXHwJtKxA=">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</latexit>© Meiji University,All rights reserved.

C2<latexit sha1_base64="cgtnFgmvq+yUCUFjoylqQOIiZMI=">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</latexit>2. (vi)<latexit sha1_base64="Tz3jCxCyONN98g1EOV5XlI3mS90=">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</latexit>

Fix(P1 P2 ) ⇢ C1 \ C2 6= ;x 2 Fix(T ) = Fix(P1 P2 ) y 2 C1 \ C2 6= ;<latexit sha1_base64="GdMIWuuWo0+Bdcw8yNxupjUbiBE=">AAADfXicpVI9b9RAEJ078xESIBfSINGYnA5RoNM6igiiipKGMh9cEimOTraZXFax18beu3CcrkbiD1BQgUSBEC38ABr+AEV+AqJMJBokeLtnFEFEQGIte2bfzpvZN54wi2WhhTioVJ0zZ8+dH7swPnHx0uXJ2tSV9SLt5hG3ojRO880wKDiWilta6pg3s5yDJIx5I9xbMucbPc4Lmar7up/xdhJ0lNyRUaABtWvX+64vlbvU9lw/CjI4s66v+KHrc5LpfsG6XauLprDLPel4pVOnci2nU5UZ8ukBpRRRlxJiUqThxxRQgWeLPBKUAdumAbAcnrTnTEMaB7eLKEZEAHQP3w52WyWqsDc5C8uOUCXGm4PpUkN8Eq/Fofgo3ojP4tsfcw1sDnOXPmw44nLWnnx6de3rX1kJrKbdY9YpjBDRp2vStEN3rBYJbZlFjMpolL/3+Nnh2t3VxuCGeCm+QN8LcSA+QKHqHUWvVnj1uc2uwNm33Ujs/RT6PwBuutuxyCPkM0iKGgzUaDB9+9nPfdQ3qmLYxPpF+XeO+cN/qmV0/E+tEX+IufN+n7KTzvps07vdnFuZqy8slhM4Rtdohm5iyuZpge7RMrVw2yf0lt7R++p3p+Hccpqj0Gql5EzTL8uZ/wG5oMi1</latexit><latexit sha1_base64="14TMkNW3mYqvhhU/1j4aRobhQsU=">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</latexit>/ C1 と仮定して矛盾を導く。
x2/ C2 ^P2 (x) 2<latexit sha1_base64="SoQ50pPqx80tRRPetqlLHOJ/vk0=">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</latexit><latexit sha1_base64="TZUoVp4OEel7/7kDedjsj1oA8oc=">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</latexit><latexit sha1_base64="Yv+wi1Id2umd+KJlkqsrTsVIP30=">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</latexit>

kP1 (P2 (x))

2yk = kP1 (P2 (x))
 hP2 (x)2

P1 (y)k<latexit sha1_base64="rKQdoFdBKzjlgLYyJ63fuZBcK2Q=">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</latexit>

P1： 堅非拡大<latexit sha1_base64="eDi142p72AtOTF8te6n62QJ39Uk=">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</latexit>

kP1 (X)

2

P1 (Y )k  hX

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y, P1 (P2 (x))
Y, P1 (X)yi

P1 (Y )i

2. (vi)<latexit sha1_base64="Tz3jCxCyONN98g1EOV5XlI3mS90=">AAADlXicpVLPa9RAFH7b+KO2ard6UPASulTqZZksRWuhUKwUb25bty00JSRxug3NTNJkdts17D/gP+DBgyh4EP8METzpyUP/hOKxghcPfjMbKVqsghOSefO9970338sL0jjKFWMHlSHrzNlz54cvjIxevHR5rDp+ZTVPOlnIW2ESJ9l64Oc8jiRvqUjFfD3NuC+CmK8FOwvav9blWR4l8pHqpXxT+G0ZbUWhrwB51buu8NV2JorFaL8/1fQcu+k1btlu3glyruwFAG7opzAativ5ru1ykaoefF61xurMLPuk4ZRGjcrVTMYrE+TSY0oopA4J4iRJwY7JpxzPBjnEKAW2SQWwDFZk/Jz6NAJuB1EcET7QHXzbOG2UqMRZ58wNO0SVGG8Gpk2T7DN7w47YB/aWHbLvf8xVmBz6Lj3swYDLU2/s6fWVb39lCeyKto9ZpzACRJ+uSdEWzRgtEbSlBtEqw0H+7pNnRyuzy5PFTfaKfYG+l+yAvYNC2f0avl7iy89NdgnOnumGMPeT6H8BXHe3bZB95NNIghocqNag+/azn3uor1XF2IWx8/LvHPP7/1RL6/ifWgN+H3Pn/D5lJ43VRt25XZ9emq7N3ysncJhu0ARNYcru0Dw9oCa1cNsX9J4+0ifrmjVn3bcWB6FDlZJzlX5Z1sMf3dzRIg==</latexit>

Fix(P1 P2 ) ⇢ C1 \ C2 6= ;x 2 Fix(T ) = Fix(P1 P2 ) y 2 C1 \ C2 6= ;<latexit sha1_base64="GdMIWuuWo0+Bdcw8yNxupjUbiBE=">AAADfXicpVI9b9RAEJ078xESIBfSINGYnA5RoNM6igiiipKGMh9cEimOTraZXFax18beu3CcrkbiD1BQgUSBEC38ABr+AEV+AqJMJBokeLtnFEFEQGIte2bfzpvZN54wi2WhhTioVJ0zZ8+dH7swPnHx0uXJ2tSV9SLt5hG3ojRO880wKDiWilta6pg3s5yDJIx5I9xbMucbPc4Lmar7up/xdhJ0lNyRUaABtWvX+64vlbvU9lw/CjI4s66v+KHrc5LpfsG6XauLprDLPel4pVOnci2nU5UZ8ukBpRRRlxJiUqThxxRQgWeLPBKUAdumAbAcnrTnTEMaB7eLKEZEAHQP3w52WyWqsDc5C8uOUCXGm4PpUkN8Eq/Fofgo3ojP4tsfcw1sDnOXPmw44nLWnnx6de3rX1kJrKbdY9YpjBDRp2vStEN3rBYJbZlFjMpolL/3+Nnh2t3VxuCGeCm+QN8LcSA+QKHqHUWvVnj1uc2uwNm33Ujs/RT6PwBuutuxyCPkM0iKGgzUaDB9+9nPfdQ3qmLYxPpF+XeO+cN/qmV0/E+tEX+IufN+n7KTzvps07vdnFuZqy8slhM4Rtdohm5iyuZpge7RMrVw2yf0lt7R++p3p+Hccpqj0Gql5EzTL8uZ/wG5oMi1</latexit><latexit sha1_base64="14TMkNW3mYqvhhU/1j4aRobhQsU=">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</latexit>/ C1 と仮定して矛盾を導く。
x2/ C2 ^P2 (x) 2<latexit sha1_base64="SoQ50pPqx80tRRPetqlLHOJ/vk0=">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</latexit><latexit sha1_base64="TZUoVp4OEel7/7kDedjsj1oA8oc=">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</latexit><latexit sha1_base64="Yv+wi1Id2umd+KJlkqsrTsVIP30=">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</latexit>

kP1 (P2 (x))

2yk = kP1 (P2 (x))
 hP2 (x)2

P1 (y)k<latexit sha1_base64="rKQdoFdBKzjlgLYyJ63fuZBcK2Q=">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</latexit>

2<latexit sha1_base64="loOUv6nMHLniaXuchU9mBCVmD/g=">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</latexit>

2

y, P1 (P2 (x))
2

kX Y k = kXk
2hX, Y i + kY k
22
2
2hX, Y i = kXk + kY k
kX Y k1
2
2
2
hX, Y i = (kXk + kY k
kX Y k )2<latexit sha1_base64="aQqU8u0pZ3tiMSron2iNyGhkd44=">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</latexit><latexit sha1_base64="A3f8OxjwMk74kyzl98ZJs5+ic/0=">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</latexit>© Meiji University,All rights reserved.

yi2. (vi)<latexit sha1_base64="Tz3jCxCyONN98g1EOV5XlI3mS90=">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</latexit>

Fix(P1 P2 ) ⇢ C1 \ C2 6= ;x 2 Fix(T ) = Fix(P1 P2 ) y 2 C1 \ C2 6= ;<latexit sha1_base64="GdMIWuuWo0+Bdcw8yNxupjUbiBE=">AAADfXicpVI9b9RAEJ078xESIBfSINGYnA5RoNM6igiiipKGMh9cEimOTraZXFax18beu3CcrkbiD1BQgUSBEC38ABr+AEV+AqJMJBokeLtnFEFEQGIte2bfzpvZN54wi2WhhTioVJ0zZ8+dH7swPnHx0uXJ2tSV9SLt5hG3ojRO880wKDiWilta6pg3s5yDJIx5I9xbMucbPc4Lmar7up/xdhJ0lNyRUaABtWvX+64vlbvU9lw/CjI4s66v+KHrc5LpfsG6XauLprDLPel4pVOnci2nU5UZ8ukBpRRRlxJiUqThxxRQgWeLPBKUAdumAbAcnrTnTEMaB7eLKEZEAHQP3w52WyWqsDc5C8uOUCXGm4PpUkN8Eq/Fofgo3ojP4tsfcw1sDnOXPmw44nLWnnx6de3rX1kJrKbdY9YpjBDRp2vStEN3rBYJbZlFjMpolL/3+Nnh2t3VxuCGeCm+QN8LcSA+QKHqHUWvVnj1uc2uwNm33Ujs/RT6PwBuutuxyCPkM0iKGgzUaDB9+9nPfdQ3qmLYxPpF+XeO+cN/qmV0/E+tEX+IufN+n7KTzvps07vdnFuZqy8slhM4Rtdohm5iyuZpge7RMrVw2yf0lt7R++p3p+Hccpqj0Gql5EzTL8uZ/wG5oMi1</latexit><latexit sha1_base64="14TMkNW3mYqvhhU/1j4aRobhQsU=">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</latexit>/ C1 と仮定して矛盾を導く。
x2/ C2 ^P2 (x) 2<latexit sha1_base64="SoQ50pPqx80tRRPetqlLHOJ/vk0=">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</latexit><latexit sha1_base64="TZUoVp4OEel7/7kDedjsj1oA8oc=">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</latexit><latexit sha1_base64="Yv+wi1Id2umd+KJlkqsrTsVIP30=">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</latexit>

kP1 (P2 (x))

2yk = kP1 (P2 (x))

2

P1 (y)k hP2 (x) y, P1 (P2 (x))
1
= {kP2 (x) yk2 + kP1 (P2 (x))
22kP2 (x) P1 (P2 (x))k }1
2
2
2
hX, Y i = (kXk + kY k
kX Y k )2<latexit sha1_base64="rKQdoFdBKzjlgLYyJ63fuZBcK2Q=">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</latexit><latexit sha1_base64="D50cKrHIqqmG18Fg8A4+PDgQ0JY=">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</latexit><latexit sha1_base64="A3f8OxjwMk74kyzl98ZJs5+ic/0=">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</latexit>© Meiji University,All rights reserved.

yiyk2

2. (vi)<latexit sha1_base64="Tz3jCxCyONN98g1EOV5XlI3mS90=">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</latexit>

Fix(P1 P2 ) ⇢ C1 \ C2 6= ;x 2 Fix(T ) = Fix(P1 P2 ) y 2 C1 \ C2 6= ;<latexit sha1_base64="GdMIWuuWo0+Bdcw8yNxupjUbiBE=">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</latexit><latexit sha1_base64="14TMkNW3mYqvhhU/1j4aRobhQsU=">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</latexit>/ C1 と仮定して矛盾を導く。
x2/ C2 ^P2 (x) 2<latexit sha1_base64="SoQ50pPqx80tRRPetqlLHOJ/vk0=">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</latexit><latexit sha1_base64="TZUoVp4OEel7/7kDedjsj1oA8oc=">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</latexit>

kP1 (P2 (x))) kP1 (P2 (x))

12yk  {kP2 (x) yk + kP1 (P2 (x))
2kP2 (x) P1 (P2 (x))k2 }2

yk2  kP2 (x)<latexit sha1_base64="u7xIUdoSItNO+HtBKogl3rq3jd4=">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</latexit>< kP2 (x)© Meiji University,All rights reserved.

yk2

yk

2

kP2 (x)

P1 (P2 (x))k2

2

>0

yk

<latexit sha1_base64="IH59dAilM6y0HbgmIM4t1hDD7E0=">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</latexit>2. (vi)<latexit sha1_base64="Tz3jCxCyONN98g1EOV5XlI3mS90=">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</latexit>

Fix(P1 P2 ) ⇢ C1 \ C2 6= ;x 2 Fix(T ) = Fix(P1 P2 ) y 2 C1 \ C2 6= ;<latexit sha1_base64="GdMIWuuWo0+Bdcw8yNxupjUbiBE=">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</latexit><latexit sha1_base64="14TMkNW3mYqvhhU/1j4aRobhQsU=">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</latexit>/ C1 と仮定して矛盾を導く。
x2/ C2 ^P2 (x) 2<latexit sha1_base64="SoQ50pPqx80tRRPetqlLHOJ/vk0=">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</latexit><latexit sha1_base64="TZUoVp4OEel7/7kDedjsj1oA8oc=">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</latexit>

kx<latexit sha1_base64="UoVzBRRiYwhE/XztQe5/BOgh5dg=">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</latexit>

yk = kP1 (P2 (x))) x 2 C2 _ P2 (x) 2 C1<latexit sha1_base64="zsFlS1cwGPg7S5aZWCF8yGr8w3g=">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</latexit>© Meiji University,All rights reserved.

yk < kP2 (x)
 kx

yk

<latexit sha1_base64="uGItTOpuiyQqYwCksQCZRPWq8H4=">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</latexit>yk矛盾

2. (vi)<latexit sha1_base64="Tz3jCxCyONN98g1EOV5XlI3mS90=">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</latexit>

Fix(P1 P2 ) ⇢ C1 \ C2 6= ;x 2 Fix(T () = Fix(P1 P2 )P2 (x) 2 C1
①x2
② x 2 C2/ C2
P2 (x) 2/ C1<latexit sha1_base64="14TMkNW3mYqvhhU/1j4aRobhQsU=">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</latexit><latexit sha1_base64="vIPDOOcc8Q81YPYcb6x/lymFaRA=">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</latexit><latexit sha1_base64="pZSAEruWQrPq+14FOEuw0xGqztk=">AAADY3icpVLLThRBFD0zjcpD5LkgMSYTJhBXkxpC1LgisnHJwwEMkEl3W4wVuqs73T0DOJkfYOvChbCAhIXxM9zwAy74ABfGJSZuWHCqpg1RIppYne5769Q999a5fb04UGkmxFmh6PTcun2nt69/4O7gvaHhkdGVNGomvqz5URAla56bykBpWctUFsi1OJFu6AVy1dueN+erLZmkKtIvsr1YboZuQ6st5bsZoZe7pQ2lS/P1mfpwWVSEXaXrTjV3ysjXQjRSmMQGXiGCjyZCSGhk9AO4SPmsowqBmNgm2sQSesqeS3TQT26TUZIRLtFtfhvcreeo5t7kTC3bZ5WAb0JmCVPis/ggzsWp+Ci+ios/5mrbHOYue7Relyvj+tD+xPKPv7JC2gyvr1g3MDxG36wpwxaeWC2K2mKLGJV+N3/rzbvz5adLU+1pcSy+Ud+ROBOfqFC3vvsni3Lpvc2uydmx3Qjt/TT73yZuutuwyC7zGSRiDUnUaDB9+9nPHdY3qgLa0Ppp/neu+J1/qmV0/E+tLr/Duav+PmXXnZWZSvVRZXZxtjz3LJ/AXtzHJB5yyh5jDs+xgBpvG+ItDnBY/OIMOKPOeDe0WMg5Y/hlOQ8uARbYvzk=</latexit><latexit sha1_base64="TZUoVp4OEel7/7kDedjsj1oA8oc=">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</latexit>

すべてのパターン①, ②
に対して証明すればよい

C1<latexit sha1_base64="ZLf7mOqzUhWQ8OvR8rdXHwJtKxA=">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</latexit>© Meiji University,All rights reserved.

C2<latexit sha1_base64="cgtnFgmvq+yUCUFjoylqQOIiZMI=">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</latexit>2. (vi) ①

x 2 Fix(T ) = Fix(P1 P2 )<latexit sha1_base64="14TMkNW3mYqvhhU/1j4aRobhQsU=">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</latexit>

P2 (x) 2 C1<latexit sha1_base64="RT6tjO8mYCJ/WOM86D27aJSgjpw=">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</latexit><latexit sha1_base64="xQ1hWCXOMVomCxHj5IH8aUcrPAM=">AAADdXicpVJNaxRBEH27ozFGzW7iRRFhyJoQL2vPEqIIgaAXj5vETQJJGGYmnXXIfDEzu9m4LN79Ax48KeQggv4IL/4BD/kJ4jFCLh583TsSNCQK9tDT1a/rVfWrLjcJ/CwX4rBUNi5cHLk0ennsytVr45XqxORqFndST7a8OIjTddfJZOBHspX7eSDXk1Q6oRvINXf3sTpf68o08+Poab6fyK3QaUf+ju85OSG7erNpN2Z7dxfMpm1xNkxuzAWzZ5p2tSbqQg/ztGEVRg3FaMYTpSlsYhsxPHQQQiJCTjuAg4zfBiwIJMS20CeW0vL1ucQAY+R26CXp4RDd5b/N3UaBRtyrmJlme8wScKZkmpgWX8Q7cSQ+i/fiq/hxZqy+jqHuss/VHXJlYlde3lg5/isr5Jrj2QnrHIZL7/M15djBA63Fp7ZEI0qlN4zfff7qaOXh8nR/RrwV36jvjTgUn6gw6n73Dpbk8msdPSJnT1cj1PeLWP8+cVXdtkZ6jKeQmDkkUaVB1e1XPfeYX6kKuIbazorXOeEP/imX0vE/uYb8AfvO+rPLThurjbo1X59bmqstPio6cBS3MIVZdtl9LOIJmmjxti9wgA/4WD42bht3jJmha7lUcK7jt2Hc+wkdPsNR</latexit>

P2 (x) = P1 P2 (x) = x
P2 (x) = x =) x 2 C2<latexit sha1_base64="AbpsX/BJVINnxsKxkEU26RFcwIg=">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</latexit>

x = P2 (x) 2 C1 =) x 2 C1<latexit sha1_base64="P4E/6MYpkUFV4jSuevxaT2KpyZM=">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</latexit>) x 2 C2 \ C1<latexit sha1_base64="2jOI2qJExbPryJzkxwZo4B8oYdA=">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</latexit>© Meiji University,All rights reserved.

2. (vi) ②

x 2 Fix(T ) = Fix(P1 P2 )x 2 C2<latexit sha1_base64="14TMkNW3mYqvhhU/1j4aRobhQsU=">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</latexit><latexit sha1_base64="pZSAEruWQrPq+14FOEuw0xGqztk=">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</latexit><latexit sha1_base64="ucCgw5670v3QauVkVJJ40c40LXk=">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</latexit>

P1 (x) = P1 P2 (x) = x =) x 2 C1<latexit sha1_base64="BtOBCgK/1zINU7ouBl47UQPLXvU=">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</latexit>) x 2 C2 \ C1<latexit sha1_base64="2jOI2qJExbPryJzkxwZo4B8oYdA=">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</latexit>) Fix(P1 P2 ) ⇢ C1 \ C2<latexit sha1_base64="aFD7gzILMoJrv0pONsb3eXFZons=">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</latexit>© Meiji University,All rights reserved.

3. (ii)

https://github.com/iidukaresearches/fixed-point© Meiji University,All rights reserved.

⾮拡⼤写像の形状

T 1 = P1 P 2 · · · Pmmm\\
Bi 6= ; =) Fix(T1 ) =Bi<latexit sha1_base64="hLIZl6IvY6td8E1Ktju9yTpe530=">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</latexit><latexit sha1_base64="XA6EjX82QoSbsRK8k9Qb6E4OTeo=">AAADoXicpVJNTxRBEK1lUBE/ALmQcJm4wXja9CBRY2JC4IK3ZXGBZBc3M2OzdujpGWd6F9fJ/gD4Ax48QcLBeOCqZy/+AQ/8BOMREy8efN07hihxNbEn0139ul5Vv+oKEikyzdhJacQZvXDx0tjl8StXr12fmJy6sZ7FnTTk9TCWcboZ+BmXQvG6FlryzSTlfhRIvhHsLJvzjS5PMxGrx7qX8K3IbyuxLUJfA2pNlpuBaId+0srFQ6//JHKXWsJtKv7cbfIo0b2MaxderMLscM8bXmGUqRjVeKp0h5r0lGIKqUMRcVKkYUvyKcPXII8YJcC2KAeWwhL2nFOfxsHtwIvDwwe6g7mNXaNAFfYmZmbZIbJI/CmYLs2xT+wNO2Uf2Vv2mX3/Y6zcxjB36WENBlyetCb2Z9a+/ZUVYdX07Iw1hBHAe7gmTdt032oR0JZYxKgMB/G7L1+drj2ozeW32CH7An0H7IR9gELV/RoerfLa6yHZO6iLLPIrILu2XpFVoPBCOXBT/7ZFXsDTIDHicKBGpansz4rv4oZGt8QaWTsr3u+M/2+5jNL/yTXg99GZ3u99eN5Yn694dysLqwvlxaWiR8dolm7SbfThPVqkFapSHbfdo2N6R++dsvPIqTq1getIqeBM0y/DafwAY2TQ8Q==</latexit><latexit sha1_base64="K22M9bF0OOpuHIdm0t31kwLoGbo=">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</latexit>

i=1<latexit sha1_base64="k2LtDV0lNPK0IrjiN7cP+qbFhn0=">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</latexit>

T 2 = P1m
X

w i Pii=2<latexit sha1_base64="fXLPPMKGVSwyq+HRIRbfwh4pvPE=">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</latexit>=) Fix(T2 ) =

⇢

!

i=1

<latexit sha1_base64="yr4eJA2gZKzGE9Mx80ybcS7MO7Y=">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</latexit>x 2 B1 :(y) :=mX

wi d(y, Bi )i=2(x) = miny2B1
B1 の部分集合で、Bi (i=2,3,…,m) に平均距離の意味で最も近い点の集まり© Meiji University,All rights reserved.

(y)2

⾮拡⼤写像の形状

T 1 = P1 P 2 · · · Pmmm\\
Bi 6= ; =) Fix(T1 ) =Bi<latexit sha1_base64="hLIZl6IvY6td8E1Ktju9yTpe530=">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</latexit><latexit sha1_base64="XA6EjX82QoSbsRK8k9Qb6E4OTeo=">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</latexit><latexit sha1_base64="K22M9bF0OOpuHIdm0t31kwLoGbo=">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</latexit>

i=1<latexit sha1_base64="+RlfsXwgdpc3Hk4zB0CP49sUpmc=">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</latexit>

m
\

i=1

i=1

Bi = ; =) Fix(T1 ) =??

© Meiji University,All rights reserved.

<latexit sha1_base64="FmwCEEmJUn7jx3n4f4uV67eMZGc=">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</latexit>

⾮拡⼤写像の形状<latexit sha1_base64="k2LtDV0lNPK0IrjiN7cP+qbFhn0=">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</latexit>

T 2 = P1m
X

w i Pii=2<latexit sha1_base64="fXLPPMKGVSwyq+HRIRbfwh4pvPE=">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</latexit>=) Fix(T2 ) =⇢!

<latexit sha1_base64="yr4eJA2gZKzGE9Mx80ybcS7MO7Y=">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</latexit>(y) :=

x 2 B1 :mX

wi d(y, Bi )2i=2(x) = miny2B1

B1 の部分集合で、Bi (i=2,3,…,m) に平均距離の意味で最も近い点の集まり<latexit sha1_base64="XA6EjX82QoSbsRK8k9Qb6E4OTeo=">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</latexit>

m
\

i=1

<latexit sha1_base64="h0EQh4TkH34fm0S5T+fWOouxOFo=">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</latexit>

Bi 6= ; =) Fix(T2 ) =© Meiji University,All rights reserved.

m
\

i=1

Bi

(y)

総括︓本講義の⽬的

q不動点とは何か︖
q不動点を⾒つけるとなぜ嬉しいのか︖という素朴な問に対する回答例の提⽰
n 講義 1: ヒルベルト空間、便利な不等式
n 講義 2: 不動点, ⾮拡⼤写像, 最適化
n 講義 3: 不動点近似法© Meiji University,All rights reserved.

最近の研究動向（多様体へ）

q深層ニューラルネットワークは通常

ユークリッド空間 (まっすぐな空間)
q⾃然⾔語処理へ応⽤する時
多様体 (曲がった空間)での最適化が必要

q8/24 13:00ー リーマン多様体上の最適化理論とその周辺
佐藤寛之先⽣© Meiji University,All rights reserved.

最近の研究動向（多様体へ）

q深層ニューラルネットワークは通常

ユークリッド空間 (まっすぐな空間)
q⾃然⾔語処理へ応⽤する時
多様体 (曲がった空間)での最適化が必要
qリーマンAdam・リーマンAMSGradの開発に成功（既存⼿法よりも⾼性能）
Hiroyuki SAKAI, H.I.: Riemannian Adaptive Optimization
Algorithms and Its Applications to Natural Language
Processing, IEEE Transactions on Cybernetics(2021)© Meiji University,All rights reserved.

最近の研究動向（多様体上の不動点問題）

q2015年 6/27: 成島先⽣、佐藤先⽣との研究打ち合わせq多様体上での⾮拡⼤写像の不動点問題
m射影ー射影先m射影積ー射影先の共通部分
mリゾルベントーゼロ点集合
m⾃然な拡張ができる

q不動点最適化アルゴリズムを多様体へ拡張
H.I., Hiroyuki SAKAI : Riemannian Stochastic Fixed Point
Optimization Algorithm, submitted© Meiji University,All rights reserved.

⽂献

q参考⽂献
m⾼橋渉著 ⾮線形・凸解析学⼊⾨ 横浜

図書© Meiji University,All rights reserved.

⽂献

q講義中に紹介した図書
mH.H.Bauschke, P.L.Combettes:

Convex Analysis and Monotone
Operator Theory in Hilbert Spaces(Second Edition), Springer 2017m⼭⽥功著 ⼯学のための関数解析 数理⼯学社
m⾼橋渉著 凸解析と不動点近似 横浜図書

© Meiji University,All rights reserved.

⽂献

q不動点理論の応⽤(ネットワーク資源割当)
mH.I.: Distributed Optimization for

Network Resource Allocation With
Nonsmooth Utility Functions, IEEE
Transactions on Control of
Network Systems 6 (4): 13541365 (2019)© Meiji University,All rights reserved.

⽂献

q不動点理論の応⽤（機械学習）
mH.I.: Stochastic Fixed Point

Optimization Algorithm for Classifier
Ensemble, IEEE Transactions on
Cybernetics 50 (10): 4370–4380 (2020)
mH.Sakai, H.I.: Riemannian Adaptive
Optimization Algorithm and Its
Application to Natural Language
Processing, IEEE Transactions on
Cybernetics (2021)© Meiji University,All rights reserved.

研究室ウェブページ
q https://iiduka.net/

以上でお終いです。
ありがとうございました。
© Meiji University,All rights reserved.