How to find maximum of a function of 2 variables

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enter
enter 2020-3-29
评论： Alex Sha 2020-4-17
I have a function z = cos(x^2 + y^2) and the assumption that both x and y belong to interval 1;5. How can I find the maximum value of the function z? I thought about using fminsearch for finding minimum of -z, but I’m new to Matlab and it doesn’t work.
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Alex Sha
Alex Sha 2020-4-17
Obviously, the maximum value of cos() should be 1, in the range of [1,5], there are multi-solutions:
1:
x: 2.32564131982953
y: 4.44118606739161
2:
x: 4.43419681301284
y: 2.33893989844493

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Star Strider
Star Strider 2020-3-29
One approach:
z = @(x,y) cos(x.^2 + y.^2);
XY = fminsearch(@(b)norm(-z(b(1),b(2))), [3; 3])
producing:
XY =
2.96385862016178
2.91449853520917
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enter
enter 2020-3-29
That's quite a sophisticated solution. is there a method like fminbnd, but for multivariable functions?
Star Strider
Star Strider 2020-3-29
I referred to it earlier: fmincon. The would be more appropriate, since it is for multivariable functions, and it allows constraints on them.

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