File:Lagrange very simple.jpg
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Lagrange_very_simple.jpg (685 × 597 pixels, file size: 66 KB, MIME type: image/jpeg)
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DescriptionLagrange very simple.jpg |
Català: Fig. 2. Il·lustració del problema d'optimització restringida.
English: Fig. 3. Illustration of the constrained optimization problem.
Italiano: Figura 3. Illustrazione del problema di ottimizzazione vincolata.
Nederlands: Afbeelding 3: eenvoudig voorbeeld.
Polski: Wykresem funkcji jest płaszczyzna. W przestrzeni trójwymiarowej, równanie opisuje walec (u którego podstawy, na płaszczyźnie leży okrąg jednostkowy). Szukanie ekstremów warunkowych sprowadza się w tym wypadku do badania punktów ekstremalnych części wspólnej walca i płaszczyzny. |
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The graph was made in Matlab with the following source code % Function data [X,Y] = meshgrid(-1.2:0.01:1.2, -1.2:0.01:1.2); Z = X+Y; % Constraint data t = -pi:0.01:pi; xc = cos(t); yc = sin(t); zc = xc+yc; % Plot graph and 'constraint' figure(); meshc(X,Y,Z); hold on; plot3(xc, yc, zc, 'k', 'LineWidth', 2); plot3(xc, yc, -3*ones(1,length(t)), 'k', 'LineWidth', 1); set(1, 'Color', [1 1 1]); set(1, 'Position', [46 107 767 682]); % Axis labels text(0.2, -2.2, -3, 'x'); text(2.0, -.3, -3, 'y'); text(-1.8, -1.5, 0, 'z'); % Annotations of the max and min points % Point indicating max plot3(sqrt(2)/2, sqrt(2)/2, 1.45, 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(sqrt(2)/2, sqrt(2)/2, -3, 'kx', 'MarkerSize', 10, 'LineWidth', 2); text('Interpreter', 'latex', 'String', '$$(\sqrt{2}/2, \sqrt{2}/2, \sqrt{2})$$',... 'Position', [.0 .3 1.9], 'FontSize', 20); % Point indicating min plot3(-sqrt(2)/2, -sqrt(2)/2, -sqrt(2), 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(-sqrt(2)/2, -sqrt(2)/2, -3, 'kx', 'MarkerSize', 10, 'LineWidth', 2); text('Interpreter', 'latex', 'String', '$$(-\sqrt{2}/2, -\sqrt{2}/2, -\sqrt{2})$$',... 'Position', [-1.4 -1.0 -1.0], 'FontSize', 20); hold off; view([34 24]); |
Author | Jacobmelgaard |
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | ||
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This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue |
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current | 13:31, 20 September 2007 | 685 × 597 (66 KB) | Loxley~commonswiki (talk | contribs) | {{Information |Description= |Source=The graph was made in Matlab with the following source code <pre> % Function data [X,Y] = meshgrid(-1.2:0.01:1.2, -1.2:0.01:1.2); Z = XY; % Constraint data t = -pi:0.01:pi; xc = cos(t); yc = sin(t); zc = xc+yc; % Plo |
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