Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
線形計画法とカーマーカー法 〜プログラマのための数学勉強会#3〜
Search
Shintaro Kaneko
May 22, 2015
Programming
3
74k
線形計画法とカーマーカー法 〜プログラマのための数学勉強会#3〜
カーマーカー法はやめて「線形計画法と整数計画法」です。
Shintaro Kaneko
May 22, 2015
Tweet
Share
More Decks by Shintaro Kaneko
See All by Shintaro Kaneko
How to keep growing SRE team at Eureka
kaneshin
3
9.3k
Go - CLI Tools Design
kaneshin
0
6.9k
Summer Internship 2018 - The principle of the eureka summer internship 2018
kaneshin
2
110
Summer Internship 2018 - The eureka summer internship 2018
kaneshin
0
100
Summer Internship 2018 - How to develop a product
kaneshin
0
87
How to write Go code
kaneshin
8
8.2k
Go Package Guidelines
kaneshin
1
1.1k
net/http package ~GoConference 2017 Spring~
kaneshin
1
2.8k
Essentials of Golang
kaneshin
5
14k
Other Decks in Programming
See All in Programming
Claude Code派?Gemini CLI派? みんなで比較LT会!_20250716
junholee
1
690
「App Intent」よくわからんけどすごい!
rinngo0302
1
120
202507_ADKで始めるエージェント開発の基本 〜デモを通じて紹介〜(奥田りさ)
risatube
PRO
3
550
構造化・自動化・ガードレール - Vibe Coding実践記 -
tonegawa07
0
150
オンコール⼊⾨〜ページャーが鳴る前に、あなたが備えられること〜 / Before The Pager Rings
yktakaha4
2
1.1k
Porting a visionOS App to Android XR
akkeylab
0
910
Android 16KBページサイズ対応をはじめからていねいに
mine2424
0
650
MDN Web Docs に日本語翻訳でコントリビュートしたくなる
ohmori_yusuke
1
130
状態遷移図を書こう / Sequence Chart vs State Diagram
orgachem
PRO
3
250
構文解析器入門
ydah
7
1.8k
Claude Code + Container Use と Cursor で作る ローカル並列開発環境のススメ / ccc local dev
kaelaela
12
7.4k
「テストは愚直&&網羅的に書くほどよい」という誤解 / Test Smarter, Not Harder
munetoshi
1
220
Featured
See All Featured
[Rails World 2023 - Day 1 Closing Keynote] - The Magic of Rails
eileencodes
35
2.5k
Done Done
chrislema
184
16k
Principles of Awesome APIs and How to Build Them.
keavy
126
17k
Build The Right Thing And Hit Your Dates
maggiecrowley
37
2.8k
XXLCSS - How to scale CSS and keep your sanity
sugarenia
248
1.3M
Responsive Adventures: Dirty Tricks From The Dark Corners of Front-End
smashingmag
251
21k
GraphQLとの向き合い方2022年版
quramy
49
14k
Why Our Code Smells
bkeepers
PRO
337
57k
Learning to Love Humans: Emotional Interface Design
aarron
273
40k
Faster Mobile Websites
deanohume
308
31k
Why You Should Never Use an ORM
jnunemaker
PRO
58
9.5k
Practical Tips for Bootstrapping Information Extraction Pipelines
honnibal
PRO
21
1.3k
Transcript
ઢܗܭը๏ͱΧʔϚʔΧʔ๏ ϓϩάϥϚͷͨΊͷֶษڧձ
ઢܗܭը๏ͱΧʔϚʔΧʔ๏
ΧʔϚʔΧʔͷ୭ಘ
ΧʔϚʔΧʔͷ୭ಘ ͑ͬʂʁ
ઢܗܭը๏ͱΧʔϚʔΧʔ๏
ઢܗܭը๏ͱܭը๏
ࣗݾհ Shintaro Kaneko ‣ גࣜձࣾΤϨΧ ‣ pairsͷ։ൃશൠ୲ ‣ ࠷ۙGoݴޠͰ։ൃ͍ͯ͠·͢ ‣
େֶ࣌ ‣ ࠷దԽͷඇઢܗܭը๏Λઐ߈ ‣ github.com/kaneshin/lbfgs ʢݹʣ ‣ ඍํఔ͕͖ࣜͩͬͨ kaneshin kaneshinth shintaro.kaneko
ࣗݾհ Shintaro Kaneko ‣ גࣜձࣾΤϨΧ ‣ pairsͷ։ൃશൠ୲ ‣ ࠷ۙGoݴޠͰ։ൃ͍ͯ͠·͢ ‣
େֶ࣌ ‣ ࠷దԽͷඇઢܗܭը๏Λઐ߈ ‣ github.com/kaneshin/lbfgs ʢݹʣ ‣ ඍํఔ͕͖ࣜͩͬͨ kaneshin kaneshinth shintaro.kaneko ٱ͠ৼΓͷֶʂ
Copyright © 2009-2015 eureka, Inc. All rights reserved.
Copyright © 2009-2015 eureka, Inc. All rights reserved.
Copyright © 2009-2015 eureka, Inc. All rights reserved. ‣ pairsϚονϯάΞϧΰϦζϜ͕ඇৗʹॏཁ
‣ ๛ͳϢʔβʔͷσʔλͷ׆༻ ‣ ΤϯδχΞ͕Ϗδωε໘͔ΒΞϧΰϦζϜΛߟ͑Δ ‣ ࣾษڧձͰRษڧʴ౷ܭֶͷษڧձ։࠵ ‣ ϏοάσʔλΛਖ਼͍ࣝ͠Ͱ༻͢Δ ‣ ౷ܭΛؒҧͬͨೝࣝͰ༻͠ͳ͍ʢภͬͨσʔλΛΘͳ͍
ຊ౷ܭͷͰ ͋Γ·ͤΜʂ
ຊͷΰʔϧ
ຊͷΰʔϧ ࠷దԽʢཧܭըʣΛ ͪΐͬͱͰͬͯΒ͏
ຊ͢͜ͱ
ຊ͢͜ͱ ΦϖϨʔγϣϯζɾϦαʔν ࠷దԽʢཧܭըʣ ઢܗܭըͱܭը
ຊΒͳ͍͜ͱ Βͳ͍͜ͱ ϓϩάϥϜͰγϛϡϨʔγϣϯ Γ͔ͨͬͨΜͰ͕͢ ͕࣌ؒݫ͍͠ͷͰׂѪ
ຊ͢͜ͱ ΦϖϨʔγϣϯζɾϦαʔν ࠷దԽʢཧܭըʣ ઢܗܭըͱܭը
ΦϖϨʔγϣϯζɾϦαʔν
ΦϖϨʔγϣϯζɾϦαʔνʢORʣ ‣ OR૬͍Λࢦ͢ ‣ ༷ʑͳܭըʹରͯ͠࠷ޮతʹͳΔΑ͏ҙࢥܾఆ͢Δ ‣ ֶɾ౷ܭతϞσϧɺΞϧΰϦζϜͷར༻ ‣ ʮγϛϡϨʔγϣϯʯͷཱ֬ORཱ͕ऀ ‣
ORͰݱ࣮ͷΛཧϞσϧʹஔ͖͑Δ ‣ ࠷దԽɼͪߦྻɼ֬ͳͲ ‣ ܉ࣄతؔ৺ͱܦࡁతؔ৺͕ڧ͍
ͭ·Γʁ
ྫ͑ɼேͷ௨ۈిं
ேͷ௨ۈిं ‣ ܦ࿏ݕࡧʹʮYahoo!࿏ઢʯ͍ͬͯΔͱࢥ͍·͢ ‣ ཪଆͰʮܦ࿏ޮʯʮίετޮʯͷߟྀ ‣ Ո͔ΒӺ·Ͱʹཁ͢Δ࣌ؒΛܭࢉ ‣ ెาӺͰిंΛͨͳ͍Α͏ʹग़ൃ͢Δܭը ‣
ࢁखઢͷَͷΑ͏ͳμΠϠ ‣ γϛϡϨʔγϣϯ͕Կສճ͞Εͨ݁Ռ
ேͷ௨ۈిं ‣ ܦ࿏ݕࡧʹʮYahoo!࿏ઢʯ͍ͬͯΔͱࢥ͍·͢ ‣ ཪଆͰʮܦ࿏ޮʯʮίετޮʯͷߟྀ ‣ Ո͔ΒӺ·Ͱʹཁ͢Δ࣌ؒΛܭࢉ ‣ ెาӺͰిंΛͨͳ͍Α͏ʹग़ൃ͢Δܭը ‣
ࢁखઢͷَͷΑ͏ͳμΠϠ ‣ γϛϡϨʔγϣϯ͕Կສճ͞Εͨ݁Ռ ͜ΕΒORͷҰछ
ׂͱۙʹOR
ຊ͢͜ͱ ΦϖϨʔγϣϯζɾϦαʔν ࠷దԽʢཧܭըʣ ઢܗܭըͱܭը
࠷దԽ
࠷దԽORͷҰཁૉ
ઢܗܭը ඇઢܗܭը ܭը ήʔϜཧ OR σʔλ ϚΠχϯά : : :
: ۚ༥ֶ ࠷దԽ
࠷దԽͱ ʢoptimization problemʣ ཧܭըͱΑΕΔ ʢMathematical Programming Problemʣ
࠷దԽͱ ༩͑ΒΕͨ݅ͷͱͰ ԿΒ͔ͷؔΛ࠷খԽɾ࠷େԽ͢Δ
࠷దԽͱ ༩͑ΒΕͨ݅ͷͱͰ ԿΒ͔ͷؔΛ࠷খԽɾ࠷େԽ͢Δ
࠷దԽͱ
࠷దԽͱ ੍݅ͷͱͰ
࠷దԽͱ ੍݅ͷͱͰɼతؔͷ
࠷దԽͱ ੍݅ͷͱͰɼతؔͷ ࠷దͱͳΔ
࠷దԽͱ ੍݅ͷͱͰɼతؔͷ ࠷దͱͳΔ࠷దղΛ
࠷దԽͱ ੍݅ͷͱͰɼతؔͷ ࠷దͱͳΔ࠷దղΛ࣮ߦՄೳྖҬ͔Β୳͢
࠷దԽͱ ੍݅ͷͱͰɼతؔͷ ࠷దͱͳΔ࠷దղΛ࣮ߦՄೳྖҬ͔Β୳͢
తؔɾ੍݅ʹΑͬͯ ࠷దԽྨ͞ΕΔ
࠷దԽͷྨʢ෦తʣ ‣ ઢܗܭը ‣ తؔɾ੍݅ͷू߹͕̍࣍ࣜͷΈ ‣ ඇઢܗܭը ‣ తؔɾ੍݅ʹඇઢܗ͕ࣜଘࡏ͢Δ ‣
ܭըʢࠞ߹ɾ७ʣ ‣ ੍݅ͷҰ෦·ͨશͯͷมͷͱΔ͕ ‣ ̎࣍ܭը ‣ త͕ؔ̎࣍ࣜɼ੍݅ͷू߹͕̍࣍ࣜ etc…
ઢܗܭը ඇઢܗܭը ܭը ήʔϜཧ OR ࠷దԽ σʔλ ϚΠχϯά : :
: : ۚ༥ֶ
ઢܗܭը ඇઢܗܭը ܭը ήʔϜཧ OR ࠷దԽ σʔλ ϚΠχϯά : :
: : ۚ༥ֶ
ຊ͢͜ͱ ΦϖϨʔγϣϯζɾϦαʔν ࠷దԽʢཧܭըʣ ઢܗܭըͱܭը
ઢܗܭը
ઢܗܭը తؔɾ੍݅ͷू߹͕̍࣍ࣜͷΈ
ྫɿੜ࢈ܭը
̎มͷੜ࢈ܭը ‣ M1, M2, M3ͷݪྉΛ༻͍ͯɼP1, P2Λੜ࢈͍ͯ͠Δ
̎มͷੜ࢈ܭը ‣ M1, M2, M3ͷݪྉΛ༻͍ͯɼP1, P2Λੜ࢈͍ͯ͠Δ ‣ ར༻ՄೳྔɿM1 ≦ 27t,
M2 ≦ 45t, M3 ≦15t
̎มͷੜ࢈ܭը ‣ M1, M2, M3ͷݪྉΛ༻͍ͯɼP1, P2Λੜ࢈͍ͯ͠Δ ‣ ར༻ՄೳྔɿM1 ≦ 27t,
M2 ≦ 45t, M3 ≦15t ‣ P1ͷੜ࢈ ‣ M1Λ2t, M2Λ8t, M3Λ3t ‣ ར५2ສʂ
̎มͷੜ࢈ܭը ‣ M1, M2, M3ͷݪྉΛ༻͍ͯɼP1, P2Λੜ࢈͍ͯ͠Δ ‣ ར༻ՄೳྔɿM1 ≦ 27t,
M2 ≦ 45t, M3 ≦15t ‣ P1ͷੜ࢈ ‣ M1Λ2t, M2Λ8t, M3Λ3t ‣ ར५2ສʂ ‣ P2ͷੜ࢈ ‣ M1Λ6t, M2Λ6t, M3Λ1t ‣ ར५5ສʂ
̎มͷੜ࢈ܭը ‣ M1, M2, M3ͷݪྉΛ༻͍ͯɼP1, P2Λੜ࢈͍ͯ͠Δ ‣ ར༻ՄೳྔɿM1 ≦ 27t,
M2 ≦ 45t, M3 ≦15t ‣ P1ͷੜ࢈ ‣ M1Λ2t, M2Λ8t, M3Λ3t ‣ ར५2ສʂ ‣ P2ͷੜ࢈ ‣ M1Λ6t, M2Λ6t, M3Λ1t ‣ ར५5ສʂ ར५Λ࠷େԽ͍ͨ͠
̎มͷੜ࢈ܭը ݪྉʘ P1 P2 ར༻Մೳྔ M1 2 6 27 M2
8 6 45 M3 3 1 15 ར५ 2 5
̎มͷੜ࢈ܭը ݪྉʘ P1 P2 ར༻Մೳྔ M1 2 6 27 M2
8 6 45 M3 3 1 15 ར५ 2 5
̎มͷੜ࢈ܭը P1, P2ͷੜ࢈ྔΛมྔ (x1, x2) ͱ͢Δͱ Λ࠷େԽͤ͞Δ࠷దԽͱͳΔ
̎มͷੜ࢈ܭը ݪྉʘ P1 P2 ར༻Մೳྔ M1 2 6 27 M2
8 6 45 M3 3 1 15 ར५ 2 5
̎มͷੜ࢈ܭը ੍݅ར༻Մೳͳݪྉͷྔͱඇෛ
̎มͷੜ࢈ܭը ੍݅ར༻Մೳͳݪྉͷྔͱඇෛ
̎มͷੜ࢈ܭը ઢܗܭըͱͯ͠ఆࣜԽ
̎มͷੜ࢈ܭը ઢܗܭըͱͯ͠ఆࣜԽ ͜ͷͷ࠷దղΛٻΊ͍ͨ
ͱ͜ΖͰ
࿈ଓ͔ʁ
ܭը
ܭը ੍݅ͷҰ෦·ͨશͯͷมͷͱΔ͕
ྫɿੜ࢈ܭըʢʣ
̎มͷੜ࢈ܭըʢʣ ‣ M1, M2, M3ͷݪྉΛ༻͍ͯɼP1, P2Λੜ࢈͍ͯ͠Δ ‣ ར༻ՄೳྔɿM1 ≦ 27t,
M2 ≦ 45t, M3 ≦15t ‣ P1ͷੜ࢈ ‣ M1Λ2t, M2Λ8t, M3Λ3t ‣ ར५2ສʂ ‣ P2ͷੜ࢈ ‣ M1Λ6t, M2Λ6t, M3Λ1t ‣ ར५5ສʂ ར५Λ࠷େԽ͍ͨ͠
̎มͷੜ࢈ܭըʢʣ ‣ M1, M2, M3ͷݪྉΛ༻͍ͯɼP1, P2Λੜ࢈͍ͯ͠Δ ‣ ར༻ՄೳྔɿM1 ≦ 27t,
M2 ≦ 45t, M3 ≦15t ‣ P1ͷੜ࢈ɹݸͰΫϨ ‣ M1Λ2t, M2Λ8t, M3Λ3t ‣ ར५2ສʂ ‣ P2ͷੜ࢈ɹݸͰΫϨ ‣ M1Λ6t, M2Λ6t, M3Λ1t ‣ ར५5ສʂ ར५Λ࠷େԽ͍ͨ͠
̎มͷੜ࢈ܭըʢʣ ‣ M1, M2, M3ͷݪྉΛ༻͍ͯɼP1, P2Λੜ࢈͍ͯ͠Δ ‣ ར༻ՄೳྔɿM1 ≦ 27t,
M2 ≦ 45t, M3 ≦15t ‣ P1ͷੜ࢈ɹݸͰΫϨ ‣ M1Λ2t, M2Λ8t, M3Λ3t ‣ ར५2ສʂ ‣ P2ͷੜ࢈ɹݸͰΫϨ ‣ M1Λ6t, M2Λ6t, M3Λ1t ‣ ར५5ສʂ ར५Λ࠷େԽ͍ͨ͠
̎มͷੜ࢈ܭըʢʣ ઢܗܭըͱͯ͠ఆࣜԽ
̎มͷੜ࢈ܭըʢʣ ઢܗܭըͱͯ͠ఆࣜԽ ͰΫϨ ͰΫϨ
̎มͷੜ࢈ܭըʢʣ ܭըͱͯ͠ఆࣜԽ
̎มͷੜ࢈ܭըʢʣ ܭըͱͯ͠ఆࣜԽ ͜ͷͷ࠷దղΛٻΊ͍ͨ
άϥϑͰΈΔղ๏ ԼهΛάϥϑͰදݱ͢Δ
None
None
ઢܗܭըͷ߹
ઢܗܭըͷ߹
ઢܗܭըͷ߹
ઢܗܭըͷ߹ ࠷దղ
ܭըͷ߹
ܭըͷ߹ ࠷దղ?
ܭըͷ߹ ࠷దղ!
ઢܗܭըͱܭըͷҧ͍ ‣ ઢܗܭըͷ࠷దղ ‣ ୯ମ๏ͱ͍͏ɺลΛḷ͍ͬͯ͘ํ๏͕࣮༻త ‣ ଟ߲ࣜ࣌ؒͰղ͚ͳ͍ͱ͖͕͋Δ ‣ ๏ͱ͍͏ղ๏ଘࡏ͢Δ ‣
࣮ߦྖҬͷ෦͔ΒղΛ୳ࡧ͢Δ ‣ ܭըͷ࠷దղ ‣ ઢܗܭըͰಘΒΕͨ࠷దղʹ͍ۙͷ͕࠷దղʹͳΒͳ͍ ߹͕͋Δ ๏ ϫγ͕ҭͯͨ
·ͱΊ
·ͱΊ ࠷దԽ ͳΜͱͳ͘ཧղͯ͠Β͑ͨͰ͠ΐ͏͔ʁ
·ͱΊ - ࠷ޙʹ ‣ ͜ͷ·ͩ·ͩϓϩάϥϜͷࢿ࢈͕গͳ͍ ‣ ཧϞσϧʹམͱͨ͢Ίʹֶͷ͕ࣝͳ͍ͱ͍͠ ‣ ઐతͳاۀ͕ಠ͍ͯ͠Δײ͕͋Δ ‣
ͦΕͧΕͷܭըߟ͑Δ͜ͱ͕ҧ͏ ‣ ݚڀ͍ͨ͠߹ΛߜΔ͖
·ͱΊ ͜ΕҎ্ͷ࠷దԽͷ γϛϡϨʔγϣϯͳͲ ୭͔͕ͬͯ͘ΕΔͱ৴͍ͯ͡·͢ʂ
Thank you :)
͓·͚ - ๏ʢΧʔϚʔΧʔ๏ʣ