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find min f(x1,x2,x3,x4) = 0.1x(1)^2+0.4x(2)^2+0.5x(3)^2+0.2x(4)^2+x(1)+2X(2)+3x(3)+x(4)+6
Find min f(x1,x2,x3,x4) and the corresponding values of x1, x2, x3, x4 subject to
2x1 + x2 + 2x3 + x4 = 5
x1 + 2x2 + 4x3 + 5x4 ≤ −21
−18 ≤ x1 ≤ 8
−20 ≤ x2 ≤ 16
−14 ≤ x3 ≤ 13
−15 ≤ x4 ≤ 5
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Aquatris
2018-9-17
There is no right or wrong way of choosing initial point, as long as initial point satisfies the constraints. One method is to solve the problem using different initial points that are randomly chosen and picking the solution that gives you the minimum function value.
Otherwise you can consider using global optimization techniques, such as genetic algorithm and particle swarm optimization.
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