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Métodos de punto interior Ejemplos
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Min z= x/2 - y 3x + 2y 6 -3x + 2y 0 x 0, y 0 Solución óptima: x =1, y = 3/2, z = -1
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x0 = 0.7000 0.4000 3.1000 1.3000 Xk = 0.7000 0 0 0 0 0.4000 0 0 0 0 3.1000 0 0 0 0 1.3000
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A = 3 2 1 0 -3 2 0 1 P A = 0.2775 0.1573 -0.2286 0.3514 0.1573 0.7811 -0.3081 -0.2266 -0.2286 -0.3081 0.2343 -0.1796 0.3514 -0.2266 -0.1796 0.7071
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function g=gradfun(x,c,alfa) n=length(x); g=alfa*c-ones(n,1)./x;
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alfa =0.6780 g=gradfun(xk,c,alfa);% Cálculo gradiente en xk g = -1.0896 -3.1780 -0.3226 -0.7692 h1=-P A *g;% Dirección de búsqueda h1 = 0.9988 2.3799 -1.2908 0.1489
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lambda = 2.7438e-004 y=e+lambda*h1; % Búsqueda lineal y = 1.0003 1.0007 0.9996 1.0000 xk=Xk*y; % Escalado, nuevo punto xk = 0.7002 0.4003 3.0989 1.3001
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Método primal- dual
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Kamarkar
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