unimore/triennale-appunti-steffo
unimore/triennale-appunti-steffo
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extracted by mini-css-extract-plugin\nmodule.exports = {\"latex\":\"latex__3Esv7\"};","import {Component} from 'preact'\nimport Split from \"../components/split\";\nimport Latex from \"../components/latex\";\nimport Panel from \"../components/panel\";\nimport Example from \"../components/example\";\nimport Todo from \"../components/todo\";\n\nconst r = String.raw;\n\nexport default class OttimizzazioneLineare extends Component {\n render() {\n return (\n <div>\n <h1>Ottimizzazione lineare intera</h1>\n <Split title={\"Materiale\"}>\n <Panel title={\"Videolezioni su YouTube\"}>\n <p>\n <b>Consigliata: <a href={\"https://www.youtube.com/playlist?list=PLh93e8qjTszffkHNn-19CqUOhHFbhBlBh\"}>Playlist con rumori di sottofondo rimossi</a></b>\n </p>\n <p>\n <a href={\"https://www.youtube.com/playlist?list=PLh0s0u9-Vwuor8YXTflVvIIU82PO1oDXS\"}>Playlist originale</a>\n </p>\n </Panel>\n <Panel title={\"Videolezioni streamate\"}>\n <ol start={\"0\"}>\n <li><a href={\"https://eu.bbcollab.com/collab/ui/session/playback/load/31427e93855c4f9cbbffe6658ee62ca5\"}>Introduzione al corso</a></li>\n <li><a href={\"https://eu.bbcollab.com/collab/ui/session/playback/load/41027969a49b4f72b0fb68ae4d9ba138\"}>Introduzione alla ricerca operativa</a></li>\n </ol>\n </Panel>\n <Panel title={\"Slides\"}>\n <ol start={\"0\"}>\n <li><a href={\"https://t.me/unimorefiles/11\"}>Introduzione al corso</a></li>\n <li><a href={\"https://t.me/unimorefiles/12\"}>Introduzione alla ricerca operativa</a></li>\n </ol>\n </Panel>\n </Split>\n <Split title={\"Le basi\"}>\n <Panel title={\"Funzione obiettivo\"}>\n <p>\n La funzione obiettivo è la funzione con valore noto sconosciuto:\n </p>\n <p>\n <Latex>{r`z = C_1 \\cdot x_1 + C_2 \\cdot x_2 + C_n \\cdot x_n`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Gradiente\"}>\n <p>\n Funzione della funzione obiettivo che indica la direzione del suo aumento più veloce.\n </p>\n <p>\n <Latex>{r`\\nabla f = \\frac{\\delta f}{\\delta x_1} e_1 + \\frac{\\delta f}{\\delta x_2} e_2 + \\frac{\\delta f}{\\delta x_n} e_n`}</Latex>\n </p>\n <p>\n <Latex>{r`e_i`}</Latex> è la direzione della coordinata i-esima.\n </p>\n <Example>\n Se <Latex>{r`n = 3`}</Latex>, allora:\n <ul>\n <li><Latex>{r`e_1 = (1, 0, 0)`}</Latex></li>\n <li><Latex>{r`e_2 = (0, 1, 0)`}</Latex></li>\n <li><Latex>{r`e_3 = (0, 0, 1)`}</Latex></li>\n </ul>\n </Example>\n <Example>\n Se la funzione obiettivo è <Latex>z = 2w + 3x + 4y</Latex>, il suo gradiente è <Latex>{r`\\nabla z = (2, 3, 4)`}</Latex>.\n </Example>\n </Panel>\n </Split>\n <Split title={\"La forma standard\"}>\n <Panel title={\"Condizioni\"}>\n <p>\n Un sistema è in <i>forma standard</i> quando ha:\n </p>\n <ul>\n <li>Solo equazioni</li>\n <li>Tutte le variabili maggiori di zero</li>\n </ul>\n </Panel>\n <Panel title={\"Slack\"}>\n <p>\n Possiamo trasformare una disequazione in equazione introducendo variabili <i>slack</i>:\n </p>\n <p>\n <Latex>{r`3x + 2y \\leq 15 \\implies 3x + 2y + s_1 = 15`}</Latex>\n </p>\n <p>\n In seguito, possiamo riscrivere tutte le funzioni in termini delle variabili slack.\n </p>\n <Example>\n Si ottiene qualcosa come <Latex>{r`z = -2 s_1 - 3 s_2 + 40`}</Latex>.\n </Example>\n </Panel>\n <Panel title={\"Tableu\"}>\n <p>\n Un modo per rappresentare sistemi in forma standard.\n </p>\n <p>\n <table class={\"right\"}>\n <thead>\n <tr>\n <th/>\n <th><Latex>x</Latex></th>\n <th><Latex>y</Latex></th>\n <th><Latex>s_1</Latex></th>\n <th><Latex>s_2</Latex></th>\n </tr>\n </thead>\n <tbody>\n <tr>\n <td>obj:</td>\n <td><Latex>80</Latex></td>\n <td><Latex>70</Latex></td>\n <td><Latex>0</Latex></td>\n <td><Latex>0</Latex></td>\n </tr>\n <tr>\n <td/>\n <td><Latex>3</Latex></td>\n <td><Latex>2</Latex></td>\n <td><Latex>1</Latex></td>\n <td><Latex>0</Latex></td>\n </tr>\n <tr>\n <td/>\n <td><Latex>2</Latex></td>\n <td><Latex>3</Latex></td>\n <td><Latex>0</Latex></td>\n <td><Latex>1</Latex></td>\n </tr>\n </tbody>\n </table>\n </p>\n <Example>\n E' la matrice equivalente completa del sistema!\n </Example>\n <p>\n Riscrivendo in termini delle variabili slack, otteniamo:\n </p>\n <p>\n <table class={\"right\"}>\n <thead>\n <tr>\n <th/>\n <th><Latex>x</Latex></th>\n <th><Latex>y</Latex></th>\n <th><Latex>s_1</Latex></th>\n <th><Latex>s_2</Latex></th>\n </tr>\n </thead>\n <tbody>\n <tr>\n <td>obj:</td>\n <td><Latex>0</Latex></td>\n <td><Latex>0</Latex></td>\n <td><Latex>-20</Latex></td>\n <td><Latex>-10</Latex></td>\n </tr>\n <tr>\n <td/>\n <td><Latex>1</Latex></td>\n <td><Latex>0</Latex></td>\n <td><Latex>{r`\\frac{3}{5}`}</Latex></td>\n <td><Latex>{r`-\\frac{2}{5}`}</Latex></td>\n </tr>\n <tr>\n <td/>\n <td><Latex>0</Latex></td>\n <td><Latex>1</Latex></td>\n <td><Latex>{r`-\\frac{2}{5}`}</Latex></td>\n <td><Latex>{r`\\frac{3}{5}`}</Latex></td>\n </tr>\n </tbody>\n </table>\n </p>\n <Example>\n Abbiamo appena applicato Gauss-Jordan, trovando la matrice inversa.\n </Example>\n </Panel>\n </Split>\n </div>\n )\n }\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"panel\":\"panel__1ubJw\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"example\":\"example__P0_NL\"};","import style from \"./todo.css\";\r\nimport { Component } from 'preact';\r\n\r\nexport default class Todo extends Component {\r\n\trender() {\r\n\t\treturn <span class={style.todo}>{this.props.children}</span>;\r\n\t}\r\n}\r\n","import style from \"./panel.css\";\nimport { Component } from 'preact';\n\nexport default class Panel extends Component {\n\tgetStyle() {\n\t\treturn style.panel;\n\t};\n\n\trender() {\n\t\tlet title = null;\n\t\tif(this.props.title !== undefined) {\n\t\t\ttitle = (<h3>{this.props.title}</h3>);\n\t\t}\n\n\t\treturn (\n\t\t\t<div class={this.getStyle()} id={this.props.id}>\n\t\t\t\t{title}\n\t\t\t\t{this.props.children}\n\t\t\t</div>\n\t\t);\n\t}\n}\n","import style from \"./example.css\";\nimport {Component} from \"preact\";\n\nexport default class Example extends Component {\n render() {\n return (\n <blockquote class={style.example}>\n {this.props.children}\n </blockquote>\n )\n }\n}\n","import style from './latex.css';\nimport { Component } from 'preact';\n\nexport default class Latex extends Component {\n\trender() {\n\t\tlet equation = `{\\\\color{White} ${this.props.children} }`;\n\t\treturn (\n\t\t\t<img src={`https://latex.codecogs.com/svg.latex?${equation}`}\n\t\t\t\t alt={this.props.children}\n\t\t\t title={this.props.children}\n\t\t\t class={style.latex}\n\t\t\t/>);\n\t}\n}","import style from \"./split.css\";\nimport { Component } from 'preact';\n\nexport default class Split extends Component {\n\trender() {\n\t let title = null;\n\t if(this.props.title !== undefined) {\n title = (<h2>{this.props.title}</h2>)\n }\n\n let children;\n if(Array.isArray(this.props.children)) {\n children = this.props.children.map(element => {\n return (<div class={style.splitchild}>{element}</div>);\n });\n }\n else {\n children = <div class={style.splitchild}>{this.props.children}</div>;\n }\n\t\treturn (\n\t <div class={style.split}>\n {title}\n <div class={style.splitparent}>{children}</div>\n </div>\n );\n\t}\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"todo\":\"todo__1pOoN\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"split\":\"split__3qCWp\",\"splitparent\":\"splitparent__2xagg\",\"splitchild\":\"splitchild__3cEoc\"};"],"sourceRoot":""}
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