solve non-linear optimization problem

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Hayam Wahdan 2021-4-26

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/813430-solve-non-linear-optimization-problem

评论： Hayam Wahdan 2021-4-28

采纳的回答： Matt J

how to maximize this nonlinear function z and find the value of x and y,

z= 0.031 {0.009[exp⁡(x-z)-1]+x/1.14}-(-1+√(1+y^4/x))/y

10<=x<=20 and y>=0

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Matt J 2021-4-26

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https://ww2.mathworks.cn/matlabcentral/answers/813430-solve-non-linear-optimization-problem#answer_684955

With fmincon, if you have Optimization Toolbox.

https://www.mathworks.com/help/optim/ug/fmincon.html

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Walter Roberson 2021-4-28

编辑：Walter Roberson 2021-4-28

在 MATLAB Online 中打开

fmincon thinks you can get an arbitrarily large result if you make y arbitrarily large.

format long g
obj = @(xyz) -xyz(3);
A = []; b = []; Aeq = []; beq = [];
lb = [10, realmin, -inf];
ub = [20 1e9 1e9];
nl = @(x,y,z) 0.031*(0.009*(exp(x-z)-1)+x./1.14)-(-1+sqrt(1+y^4./x))./y - z
nl = function_handle with value:
    @(x,y,z)0.031*(0.009*(exp(x-z)-1)+x./1.14)-(-1+sqrt(1+y^4./x))./y-z
nonlcon = @(xyz) deal(nl(xyz(1), xyz(2), xyz(3)), []);
xyz0 = [.1 .2 .3]
xyz0 = 1×3
                       0.1                       0.2                       0.3
[best, fval] = fmincon(obj, xyz0, A, b, Aeq, beq, lb, ub, nonlcon)
Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.
best = 1×3
          17.9264664551072          190469849.537475          999999999.999999
fval = 
         -999999999.999999