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<html>
<head>
<title>Interactive Systems Optimization Comparison | Ezequiel Leonardo Castaño Personal Website</title>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="google-site-verification" content="" />
<!-- Feed -->
<link rel="alternate" type="application/atom+xml" href="http://feeds.feedburner.com/ELCWEB"
title="Ezequiel Leonardo Castaño Personal Website Atom Feed" />
<link rel="alternate" type="application/atom+xml" href="http://feeds.feedburner.com/feeds/all.atom.xml"
title="Ezequiel Leonardo Castaño Personal Website Atom Feed" />
<!-- FAVICON -->
<link rel="apple-touch-icon" sizes="180x180" href="/apple-touch-icon.png">
<link rel="icon" type="image/png" sizes="32x32" href="/favicon-32x32.png">
<link rel="icon" type="image/png" sizes="16x16" href="/favicon-16x16.png">
<link rel="manifest" href="/site.webmanifest">
<link rel="mask-icon" href="/safari-pinned-tab.svg" color="#000000">
<meta name="msapplication-TileColor" content="#000000">
<meta name="theme-color" content="#ffffff">
<!-- Social -->
<meta property="article:author" content="Ezequiel Leonardo Castaño" />
<meta property="article:section" content="Programming" />
<meta property="article:published_time" content="2019-11-17" />
<meta property="og:type" content="website" />
<meta property="og:title" content="Interactive Systems Optimization Comparison | Ezequiel Leonardo Castaño Personal Website" />
<meta property="og:description" content="A visualization tool that shows different Systems Optimization Methods with 2 Variables" />
<meta property="og:site_name" content="Ezequiel Leonardo Castaño Personal Website" />
<meta property="og:url" content="https://elc.github.io/systems-optimization-methods/" />
<meta property="og:image" content="https://elc.github.io/systems-optimization-methods/media_image.png" />
<meta name="twitter:card" content="summary">
<meta name="twitter:title" content="Interactive Systems Optimization Comparison | Ezequiel Leonardo Castaño Personal Website">
<meta name="twitter:description" content="A visualization tool that shows different Systems Optimization Methods with 2 Variables">
<meta name="twitter:url" content="https://elc.github.io/systems-optimization-methods/">
<meta name="twitter:image" content="https://elc.github.io/systems-optimization-methods/media_image.png">
<script src="https://elc.github.io/interactive-optimization/nerdamer.js"></script>
<!-- LOAD ADD-ONS -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/d3/3.5.17/d3.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/function-plot/1.18.1/function-plot.js"></script>
<link href="https://fonts.googleapis.com/css?family=M+PLUS+1p&display=swap" rel="stylesheet">
<link rel="stylesheet" type="text/css" href='https://elc.github.io/interactive-optimization/style.css'>
<style>
.header{
display:flex;
flex-direction: column;
justify-content: space-between;
}
.header__title{
margin: 0 0 15px 0;
}
.content{
margin: 15px 0 10px 0;
}
.window{
padding: 12px;
}
.option--results{
padding: 5px 10px 10px 10px;
}
.option--plot{
padding-top: 0;
}
.header__input--point{
width: 35px;
}
</style>
<script src="https://elc.github.io/interactive-optimization/basic.js"></script>
<script>
function method(fun, evaluate_point, iterations){
var alpha = document.querySelector("#alpha").value;
var beta = document.querySelector("#beta").value;
var iteration_description = "";
const guess_x_fix = document.querySelector("#guess_x").value;
const guess_y_fix = document.querySelector("#guess_y").value;
result = newton_method(fun, evaluate_point, iterations)
var [x_value, y_value, z_value] = result.values
iteration_description += get_text(x_value, y_value, z_value, colors[0], "Newton");
evaluate_point = {'x': guess_x_fix, 'y': guess_y_fix};
result = newton_method_with_alpha(fun, evaluate_point, alpha, iterations)
var [x_value, y_value, z_value] = result.values
iteration_description += get_text(x_value, y_value, z_value, colors[1], "Newton With Alpha");
evaluate_point = {'x': guess_x_fix, 'y': guess_y_fix};
result = gradient_method(fun, evaluate_point, alpha, iterations)
var [x_value, y_value, z_value] = result.values
iteration_description += get_text(x_value, y_value, z_value, colors[2], "Gradient Descent");
evaluate_point = {'x': guess_x_fix, 'y': guess_y_fix};
result = levenberg_marquardt_method(fun, evaluate_point, beta, iterations)
var [x_value, y_value, z_value] = result.values
iteration_description += get_text(x_value, y_value, z_value, colors[3], "Levenberg-Marquard");
evaluate_point = {'x': guess_x_fix, 'y': guess_y_fix};
result = BFGS(fun, evaluate_point, alpha, iterations)
var [x_value, y_value, z_value] = result.values
iteration_description += get_text(x_value, y_value, z_value, colors[4], "Quasi-Newton (BFGS)");
return {
'description': iteration_description
}
}
function test_function(fun, guess_x, guess_y, alpha, beta, iterations) {
document.querySelector("#function").value = fun;
document.querySelector("#guess_x").value = guess_x;
document.querySelector("#guess_y").value = guess_y;
document.querySelector("#alpha").value = alpha;
document.querySelector("#beta").value = beta;
document.querySelector("#iterations").selectedIndex = iterations - 1;
plot();
}
</script>
</head>
<body class="frame--main">
<header class="header window">
<h1 class="header__title">Systems Optimization Comparison</h1>
<section class="header__settings">
<div class="header__settings__component">
<label for="function">Function f(x, y) </label>
<span class='header__settings__component__field'>
<span class="header__settings__label">f(x, y)=</span>
<input class="header__input--function" id="function" type="text" value="0.1(3 * x^2 + 2 * x * y + 1.5 * y^2)"
onkeypress="plot_event(event)">
</span>
</div>
<div class="header__settings__component">
<label for="guess">Parameters</label>
<span class='header__settings__component__field'>
<span class="header__settings__label">X<sub>0</sub>=</span>
<input class="header__input--point" id="guess_x" type="float" value="2" onkeypress="plot_event(event)">
<span class="header__settings__label">Y<sub>0</sub>=</span>
<input class="header__input--point" id="guess_y" type="float" value="-3" onkeypress="plot_event(event)">
<span class="header__settings__label">α=</span>
<input class="header__input--point" id="alpha" type="float" value="1" onkeypress="plot_event(event)">
<span class="header__settings__label">β=</span>
<input class="header__input--point" id="beta" type="float" value="1" onkeypress="plot_event(event)">
</span>
</div>
<div class="header__settings__component">
<label for="iterations">Iterations</label>
<span class='header__settings__component__field'>
<select class="header__input--iteration" id="iterations" name="iterations">
<option value="1">1</option>
<option value="2">2</option>
<option value="3">3</option>
<option value="4">4</option>
<option value="5">5</option>
<option value="6">6</option>
<option value="7" selected>7</option>
</select>
</span>
</div>
<button class="button button--calculate" type="submit" onclick="plot();">Calculate!</button>
</section>
</header>
<div class="content">
<section class="option window option--results">
<p id="results"></p>
</section>
<section class="option window option--plot">
<div id="graph"></div>
<p class="option--results__measurements" id="exec-time"></p>
</section>
<section class="option window option--test">
<p class="option__title"> Try These Functions</p>
<button class="button button--function"
onclick="test_function('0.02 * ( (x^2 + y - 11)^2 + (x + y^2 - 7)^2)', 1, 1, 1, 1, 5);">Quartic<br><small>(Himmelblau)</small></button>
<button class="button button--function"
onclick="test_function('2*(0.5 * x)^2 - 1.05 * (0.5 * x)^4 + (0.5 * x)^6 / 6 + (0.5 * x) * (0.75 * y) + (0.75 * y)^2', -0.8, -4, 0.7, 1, 3);">Local
Minima<br><small>(Camel)</small></button>
<button class="button button--function" onclick="test_function('(0.4 * x)^3 + (0.3 * y)^5', 5, 5, 0.8, 1, 7);">Saddle Point
<br><small>(Powell Sum)</small></button>
<button class="button button--function"
onclick="test_function('0.01 * ((x^2 - 1)^2 + (y^2 - 2)^2)', 2, -3, 1, 1, 5);">Multi
Modal<br><small>(Qing)</small></button>
<button class="button button--function"
onclick="test_function('0.0005 * (100 (y - (0.5 * x)^2)^2+ (1 - (0.5 * x))^2)', -1.2, 1, 2, 1, 4);">Local
Minima<br><small>(Rosenbrock)</small></button>
<a href="https://forms.gle/wJkGp2iGApzM19W69" class="button button--propose button--function" target="_blank">Propose</a>
</section>
</div>
<footer class="footer window">
<p>
This project was an assignment for the course <a
href="https://www.tu-ilmenau.de/en/process-optimization/teaching/vorlesungen-seminare-und-praktika/wintersemester/">Systems
Optimization</a> in the <a href="https://www.tu-ilmenau.de/">TU Ilmenau</a>
<br>
Developed by <a href="https://elc.github.io">Ezequiel Leonardo Castaño</a>
</p>
</footer>
</body>
</html>