MATLAB: Solving non linear system

nonlinearoptimization

I'm trying to solve a non-linear min-max systems using the below code. and i'm geeting this error
Error using symengine
Input arguments must be convertible to floating-point numbers.
Error in sym/privBinaryOp (line 1030)
Csym = mupadmex(op,args{1}.s, args{2}.s, varargin{:});
Error in sym/min (line 78)
C = privBinaryOp(X, Y, 'symobj::zipWithImplicitExpansion', 'symobj::minComplex');
Any suggestions to fix it?
syms x111 x114 x121 x124 x211 x214 x221 x224
eq1 = min((min(3*x111,8*x111)+min(2*x211,11*x211)),(6*min(3*x111,8*x111)+6*min(2*x211,11*x211)))+min((7*min(3*x121,8*x121)+7*min(2*x221,11*x221)),(-3*max(3*x124,8*x124)-3*max(2*x224,11*x224)))+min((2*min(x111,7*x111)+2*min(3*x211,7*x211)),(-5*max(x114,7*x114)-5*max(3*x214,7*x214)))+min((min(x121,7*x121)+min(3*x221,7*x221)),(5*min(x121,7*x121)+5*min(2*x221,7*x221)))==-964;
eq2 = min ((6* min (3* x111, 8 *x111)+6* min (2* x211, 11 *x211)),(-max (3*x114, 8* x114) -max (2* x214, 11* x214)))+min ((min (3 *x121, 8* x121)+min (2* x221, 11* x221)),(7* min (3* x121, 8* x121)+7 *min (2 *x221, 11 *x221)))+ min ((3 *min (x111, 7* x111)+3 *min (3* x211, 7* x211)), (6 *min (x111, 7* x111)+6* min (3 *x211, 7* x211)))+min ((4 *min (x121, 7 *x121) +4 *min (3* x221, 7* x221)),(-3 *max (x124, 7 *x124) -3* max (3* x224, 7 *x224)))== -793;
eq3 = min ((min (-8 *x114, -x114) +min (-4 *x214, 6* x211)), (6 *min (-8* x114, -x114) +6 *min (-4* x214, 6* x211)))+min ((7* min (-8* x124, -x124) +7* min (-4* x224, 6* x221)), (-3* max (-x121, -8* x121) -3* max (6* x224, -4* x221)))+min ((2* min (-5* x114, -x114) +2* min (-6 *x214, 2* x211)), (-5* max (-x111, -5* x111) -5* max (2* x214, -6* x211)))+min ((min (-5* x124, -x124) +min (-6* x224, 2* x221)), (5* min (-5* x124, -x124) +5 *min (-6* x224, 2* x221))) == -1331;
eq4 = min ((6* min (-8* x114, -x114) +6* min (-4 *x214, 6* x211)), (-max (-x111, -8* x111) -max (6* x214, -4* x211)))+min ((min (-8* x124, -x124) +min (-4 *x224, 6* x221)), (7* min (-8* x124, -x124) +7 *min (-4* x224, 6* x221)))+min ((3* min (-5* x114, -x114) +3* min (-6* x214, 2* x211)), (6* min (-5* x114, -x114) +6* min (-6* x214, 2* x211)))+min ((4* min (-5 *x124, -x124) +4* min (-6* x224, 2* x221)), (-3* max (-x121, -5* x121) -3* max (2* x224, -6* x221))) == -1476;
eq5 = max ((max (3* x114, 8* x114) +max (2* x214, 11* x214)), (6* max (3* x114, 8* x114) +6 *max (2 *x214, 11 *x214)))+max ((-3 *min (3 *x121, 8* x121) -3* min (2 *x221, 11* x221)), (7 *max (3* x124, 8* x124) +7* max (2* x224, 11* x224)))+max ((-5* min (x111, 7* x111) -5 *min (3* x211, 7* x211)), (2 *max (x114, 7 *x114) + 2* max (3* x214, 7* x214)))+max ((max (x124, 7 *x124) +max (3 *x224, 7* x224)), (5 *max (x124, 7* x124) +5 *max (3 *x224, 7* x224))) == 1816;
eq6 = max ((-min (3* x111, 8* x111) -min (2* x211, 11* x211)), (6* max (3* x114, 8* x114) +6 *max (2* x214, 11* x214)))+max ((max (3* x124, 8* x124) +max (2* x224, 11* x224)), (7 *max (3 *x124, 8* x124) +7* max (2* x224, 11* x224)))+max ((3* max (x114, 7* x114) +3 *max (3 *x214, 7* x214)), (6* max (x114, 7* x114) +6* max (3 *x214, 7* x214)))+max ((-3* min (x121, 7* x121) -3* min (3 *x221, 7* x221)), (4* max (x124, 7* x124) +4* max (3 *x224, 7 *x224))) == 2019;
eq7 = max ((max (-x111, -8* x111) +max (6 *x214, -4 *x211)), (6* max (-x111, -8* x111) +6* max (6 *x214, -4 *x211)))+max ((-3* min (-8* x124, -x124) -3 *min (-4* x224, 6 *x221)), (7 *max (-x121, -8* x121) +7 *max (6 *x224, -4* x221)))+max ((-5* min (-5* x114, -x114) -5 *min (-6 *x214, 2* x211)), (2* max (-x111, -5* x111) +2 *max (2* x214, -6* x211)))+max ((max (-x121, -5 *x121) +max (2* x224, -6 *x221)), (5* max (-x121, -5 *x121) +5 *max (2 *x224, -6* x221))) == 968;
eq8 = max ((-min (-8 *x114, -x114) -min (-4 *x214, 6 *x211)), (6* max (-x111, -8* x111) +6* max (6* x214, -4 *x211)))+max ((max (-x121, -8 *x121) +max (6* x224, -4* x221)), (7 *max (-x121, -8 *x121) +7 *max (6* x224, -4* x221)))+max ((3 *max (-x111, -5 *x111) +3 *max (2* x214, -6 *x211)), (6 *max (-x111, -5* x111) +6* max (2 *x214, -6 *x211)))+max ((-3* min (-5* x124, -x124) -3 *min (-6* x224, 2* x221)), (4* max (-x121, -5 *x121) +4 *max (2 *x224, -6 *x221))) == 843;
        
sol = fsolve([eq1 eq2 eq3 eq4 eq5 eq6 eq7 eq8], [x111 x114 x121 x124 x211 x214 x221 x224]);
x1Sol = sol.x111;
x2Sol = sol.x114;
x3Sol = sol.x121;
x4Sol = sol.x124;
x5Sol = sol.x211;
x6Sol = sol.x214;
x7Sol = sol.x221;
x8Sol = sol.x224;

Best Answer

syms x111 x114 x121 x124 x211 x214 x221 x224
min = @(A,B) piecewise(A<=B, A, B)
max = @(A,B) piecewise(A>=B, A, B)
eq1 = min((min(3*x111,8*x111)+min(2*x211,11*x211)),(6*min(3*x111,8*x111)+6*min(2*x211,11*x211)))+min((7*min(3*x121,8*x121)+7*min(2*x221,11*x221)),(-3*max(3*x124,8*x124)-3*max(2*x224,11*x224)))+min((2*min(x111,7*x111)+2*min(3*x211,7*x211)),(-5*max(x114,7*x114)-5*max(3*x214,7*x214)))+min((min(x121,7*x121)+min(3*x221,7*x221)),(5*min(x121,7*x121)+5*min(2*x221,7*x221)))==-964;
eq2 = min ((6* min (3* x111, 8 *x111)+6* min (2* x211, 11 *x211)),(-max (3*x114, 8* x114) -max (2* x214, 11* x214)))+min ((min (3 *x121, 8* x121)+min (2* x221, 11* x221)),(7* min (3* x121, 8* x121)+7 *min (2 *x221, 11 *x221)))+ min ((3 *min (x111, 7* x111)+3 *min (3* x211, 7* x211)), (6 *min (x111, 7* x111)+6* min (3 *x211, 7* x211)))+min ((4 *min (x121, 7 *x121) +4 *min (3* x221, 7* x221)),(-3 *max (x124, 7 *x124) -3* max (3* x224, 7 *x224)))== -793;
eq3 = min ((min (-8 *x114, -x114) +min (-4 *x214, 6* x211)), (6 *min (-8* x114, -x114) +6 *min (-4* x214, 6* x211)))+min ((7* min (-8* x124, -x124) +7* min (-4* x224, 6* x221)), (-3* max (-x121, -8* x121) -3* max (6* x224, -4* x221)))+min ((2* min (-5* x114, -x114) +2* min (-6 *x214, 2* x211)), (-5* max (-x111, -5* x111) -5* max (2* x214, -6* x211)))+min ((min (-5* x124, -x124) +min (-6* x224, 2* x221)), (5* min (-5* x124, -x124) +5 *min (-6* x224, 2* x221))) == -1331;
eq4 = min ((6* min (-8* x114, -x114) +6* min (-4 *x214, 6* x211)), (-max (-x111, -8* x111) -max (6* x214, -4* x211)))+min ((min (-8* x124, -x124) +min (-4 *x224, 6* x221)), (7* min (-8* x124, -x124) +7 *min (-4* x224, 6* x221)))+min ((3* min (-5* x114, -x114) +3* min (-6* x214, 2* x211)), (6* min (-5* x114, -x114) +6* min (-6* x214, 2* x211)))+min ((4* min (-5 *x124, -x124) +4* min (-6* x224, 2* x221)), (-3* max (-x121, -5* x121) -3* max (2* x224, -6* x221))) == -1476;
eq5 = max ((max (3* x114, 8* x114) +max (2* x214, 11* x214)), (6* max (3* x114, 8* x114) +6 *max (2 *x214, 11 *x214)))+max ((-3 *min (3 *x121, 8* x121) -3* min (2 *x221, 11* x221)), (7 *max (3* x124, 8* x124) +7* max (2* x224, 11* x224)))+max ((-5* min (x111, 7* x111) -5 *min (3* x211, 7* x211)), (2 *max (x114, 7 *x114) + 2* max (3* x214, 7* x214)))+max ((max (x124, 7 *x124) +max (3 *x224, 7* x224)), (5 *max (x124, 7* x124) +5 *max (3 *x224, 7* x224))) == 1816;
eq6 = max ((-min (3* x111, 8* x111) -min (2* x211, 11* x211)), (6* max (3* x114, 8* x114) +6 *max (2* x214, 11* x214)))+max ((max (3* x124, 8* x124) +max (2* x224, 11* x224)), (7 *max (3 *x124, 8* x124) +7* max (2* x224, 11* x224)))+max ((3* max (x114, 7* x114) +3 *max (3 *x214, 7* x214)), (6* max (x114, 7* x114) +6* max (3 *x214, 7* x214)))+max ((-3* min (x121, 7* x121) -3* min (3 *x221, 7* x221)), (4* max (x124, 7* x124) +4* max (3 *x224, 7 *x224))) == 2019;
eq7 = max ((max (-x111, -8* x111) +max (6 *x214, -4 *x211)), (6* max (-x111, -8* x111) +6* max (6 *x214, -4 *x211)))+max ((-3* min (-8* x124, -x124) -3 *min (-4* x224, 6 *x221)), (7 *max (-x121, -8* x121) +7 *max (6 *x224, -4* x221)))+max ((-5* min (-5* x114, -x114) -5 *min (-6 *x214, 2* x211)), (2* max (-x111, -5* x111) +2 *max (2* x214, -6* x211)))+max ((max (-x121, -5 *x121) +max (2* x224, -6 *x221)), (5* max (-x121, -5 *x121) +5 *max (2 *x224, -6* x221))) == 968;
eq8 = max ((-min (-8 *x114, -x114) -min (-4 *x214, 6 *x211)), (6* max (-x111, -8* x111) +6* max (6* x214, -4 *x211)))+max ((max (-x121, -8 *x121) +max (6* x224, -4* x221)), (7 *max (-x121, -8 *x121) +7 *max (6* x224, -4* x221)))+max ((3 *max (-x111, -5 *x111) +3 *max (2* x214, -6 *x211)), (6 *max (-x111, -5* x111) +6* max (2 *x214, -6 *x211)))+max ((-3* min (-5* x124, -x124) -3 *min (-6* x224, 2* x221)), (4* max (-x121, -5 *x121) +4 *max (2 *x224, -6 *x221))) == 843;
eqns = [eq1 eq2 eq3 eq4 eq5 eq6 eq7 eq8]
EQFUN = matlabFunction(eqns, 'vars', {[x111 x114 x121 x124 x211 x214 x221 x224]}, 'file', 'q744767_eqns.m', 'optimize', false)
!cat q744767_eqns.m
sol = fsolve(EQFUN, [x111 x114 x121 x124 x211 x214 x221 x224]);
x1Sol = sol.x111;
x2Sol = sol.x114;
x3Sol = sol.x121;
x4Sol = sol.x124;
x5Sol = sol.x211;
x6Sol = sol.x214;
x7Sol = sol.x221;
x8Sol = sol.x224;
Execution might take a while... A long while. Just to build the function properly :(
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