# Solve Inequality with inequality constraints

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Nikolas Spiliopoulos on 10 Jul 2020
Commented: Walter Roberson on 10 Jul 2020
Hi there,
i am trying to "solve" an inequality (actually looking for the area of possibel solutions), I have tried this.
syms I I_opt
a=0.1735;
b=0.1967;
c=0.2137;
d=0.2856;
eq_1=I>=0;
eq_2=I_opt>=0;
eq_3=I<=4.67;
eq_4=I_opt<=4.67;
eq_5=a/c*exp(b*I-d*I_opt)*(1-a*exp(b*I))/(1-c*exp(d*I_opt))>1;
eqns=[eq_1 eq_2 eq_3 eq_4 eq_5];
S=solve(eqns,[I I_opt])
Which is actually inequality 5, with 0<=I,I_opt<=4,67;
I get a struct with zero size, although it seems there are solutions for the equations, do you know why?
thanks!!
Walter Roberson on 10 Jul 2020
Two disconnected triangles. They both fit inside I = 0 to 4.67, I_opt = 0 to 4.67 (

Walter Roberson on 10 Jul 2020
There is no symbolic solution; the equations are too complicated for that.
syms I I_opt real
Q = @(v) sym(v);
a = Q(0.1735);
b = Q(0.1967);
c = Q(0.2137);
d = Q(0.2856);
eq_1 = I >= Q(0);
eq_2 = I_opt >= Q(0);
eq_3 = I <= Q(4.67);
eq_4 = I_opt <= Q(4.67);
eq_5 = a/c*exp(b*I-d*I_opt)*(1-a*exp(b*I))/(1-c*exp(d*I_opt)) > Q(1);
eqns = [eq_1, eq_2, eq_3, eq_4, eq_5];
S = solve(eqns,[I I_opt], 'returnconditions', true);
disp(S)
[Ig, IoG] = ndgrid(linspace(0,4.7,200));
EQ1 = double(subs(eq_1,{I,I_opt},{Ig, IoG}));
EQ2 = double(subs(eq_2,{I,I_opt},{Ig, IoG}));
EQ3 = double(subs(eq_3,{I,I_opt},{Ig, IoG}));
EQ4 = double(subs(eq_4,{I,I_opt},{Ig, IoG}));
EQ5 = double(subs(eq_5,{I,I_opt},{Ig, IoG}));
mask = EQ1 & EQ2 & EQ3 & EQ4 & EQ5;
Walter Roberson on 10 Jul 2020
syms I I_opt real
Q = @(v) sym(v);
a = Q(0.1735);
b = Q(0.1967);
c = Q(0.2137);
d = Q(0.2856);
eq_1 = I >= Q(0);
eq_2 = I_opt >= Q(0);
eq_3 = I <= Q(4.67);
eq_4 = I_opt <= Q(4.67);
eq_5_L = a/c*exp(b*I-d*I_opt)*(1-a*exp(b*I))/(1-c*exp(d*I_opt));
eq_5 = eq_5_L > Q(1);
%eqns = [eq_1, eq_2, eq_3, eq_4, eq_5];
%S = solve(eqns,[I I_opt], 'returnconditions', true);
%disp(S)
[Ig, IoG] = ndgrid(linspace(0,4.7,200));
EQ1 = double(subs(eq_1,{I,I_opt},{Ig, IoG}));
EQ2 = double(subs(eq_2,{I,I_opt},{Ig, IoG}));
EQ3 = double(subs(eq_3,{I,I_opt},{Ig, IoG}));
EQ4 = double(subs(eq_4,{I,I_opt},{Ig, IoG}));
EQ5_L = double(subs(eq_5_L,{I,I_opt},{Ig, IoG}));
EQ5 = EQ5_L > 1;
mask = EQ1 & EQ2 & EQ3 & EQ4 & EQ5;
z = nan(size(EQ5_L));
surf(Ig, IoG, z, 'edgecolor','none')