How to solve this optimization problems for different values of lambda>0?

Dear All,

How can I solve the attached optimization problem for different values ​​of.

[John D'Errico]

Use fmincon. Why not try it?

[Rajkumar Verma]

I have tried with this code by taking lambda=2. But system is showing error (Unable to perform assignment because dot indexing is not supported for variables of this type.)

lb = [0 0 0 0];

Aeq = [1 1 1 0];

beq = 1;

x0 = [1 1 1 4] / 3;

fun = @ObjectiveFunction;

Nonlcon = @NLcon;

A = [];

b = [];

ub = [];

[X, FVAL] = fmincon (fun, x0, A, b, t, Aeq, beq, lb, ub, Nonlcon)

function f = ObjectiveFunction (x)

f =-(x(4));

end

function [C, Ceq] = NLcon (x)

C(1)= -(((((4)^2)*x(1)+((4)^2)*x(2)+((3.4)^2)*x(3))^(1/2))-x(4));

C(2)= -(((((4)^2)*x(1)+((2.6)^2)*x(2)+((6)^2)*x(3))^(1/2))-x(4));

C(3)= -(((((3)^2)*x(1)+((5.9)^2)*x(2)+((4)^2)*x(3))^(1/2))-x(4));

C(4)= -(((((3)^2)*x(1)+((4)^2)*x(2)+((4)^2)*x(3))^(1/2))-x(4));

C(5)= -(((((4.3)^2)*x(1)+((0)^2)*x(2)+((4)^2)*x(3))^(1/2))-x(4));

Ceq= [];

end