Is it possible to have binary and continuous variables in fmincon?

Hello I am beginner in Matlab Optimization. I want to minimize a function depending on a two matrices of variables (x(1)-x(72) continues variables and x(73)-x(90) binary variables). The code is the following.

function [c, ceq] = confun(x)
dA1=5;
dA2=9;
dB1=7;
dB2=7;
dC1=10;
dC2=5;
k=2;
% Nonlinear inequality constraints
c = [   x(73)+x(74)+x(75)+x(76)+x(77)+x(78)-k;
        x(79)+x(80)+x(81)+x(82)+x(83)+x(84)-k;
        x(85)+x(86)+x(87)+x(88)+x(89)+x(90)-k;
         x(1)-dA1*x(73);
         x(2)-dA1*x(79);
         x(13)-dA1*x(74);
         x(14)-dA1*x(80);
         x(25)-dA1*x(75);
         x(26)-dA1*x(81);
         x(37)-dA1*x(76);
         x(38)-dA1*x(79);
         x(49)-dA1*x(77);
         x(50)-dA1*x(83);
         x(61)-dA1*x(78);
         x(62)-dA1*x(84); 
         x(3)-dB1*x(73);
         x(4)-dB1*x(79); 
         x(15)-dB1*x(74);  
         x(16)-dB1*x(80);  
         x(27)-dB1*x(75);  
         x(28)-dB1*x(81);  
         x(39)-dB1*x(76);  
         x(40)-dB1*x(82);  
         x(51)-dB1*x(77);  
         x(52)-dB1*x(83);  
         x(63)-dB1*x(78);  
         x(64)-dB1*x(84);
         x(5)-dC1*x(73);
         x(6)-dC1*x(79);
         x(17)-dC1*x(74);
         x(18)-dC1*x(80);
         x(29)-dC1*x(75);
         x(30)-dC1*x(81);
         x(41)-dC1*x(76);
         x(42)-dC1*x(82);
         x(53)-dC1*x(77);
         x(54)-dC1*x(83);
         x(65)-dC1*x(78);
         x(66)-dC1*x(84); 
         x(7)-dA2*x(79);
         x(8)-dA2*x(85);
         x(19)-dA2*x(80);
         x(20)-dA2*x(86);
         x(31)-dA2*x(81);
         x(32)-dA2*x(87);
         x(43)-dA2*x(82);
         x(44)-dA2*x(88);
         x(55)-dA2*x(83);
         x(56)-dA2*x(89);
         x(67)-dA2*x(84);
         x(68)-dA2*x(90); 
         x(9)-dB2*x(79);
         x(10)-dB2*x(85);
         x(21)-dB2*x(80);
         x(22)-dB2*x(86);
         x(33)-dB2*x(81);
         x(34)-dB2*x(87);
         x(45)-dB2*x(82);
         x(46)-dB2*x(88);
         x(57)-dB2*x(83);
         x(58)-dB2*x(89);
         x(69)-dB2*x(84);
         x(70)-dB2*x(90); 
         x(11)-dC2.x(79);
         x(12)-dC2.x(85);
         x(23)-dC2.x(80);
         x(24)-dC2*x(86);
         x(35)-dC2*x(81);
         x(36)-dC2*x(87);
         x(47)-dC2*x(82);
         x(48)-dC2*x(88);
         x(59)-dC2*x(83);
         x(60)-dC2*x(89);
         x(71)-dC2*x(84);
         x(72)-dC2*x(90); 
        x(1) + x(3) + x(5)-15;
        x(7) + x(9) + x(11) + x(2) + x(4)+ x(6)-15;
        x(8) + x(10) + x(12)-15; 
        x(13) + x(15) + x(17)-15;
        x(19) + x(21) + x(23) + x(14) + x(16)+ x(18)-15;
        x(20) + x(22) + x(24)-15; 
        x(25) + x(27) + x(29)-15;
        x(31) + x(33) + x(35) + x(26) + x(28)+ x(30)-15;
        x(32) + x(34) + x(36)-15; 
        x(37) + x(39) + x(41)-15;
        x(43) + x(45) + x(47) + x(38) + x(40)+ x(42)-15;
        x(44) + x(46) + x(48)-15; 
        x(49) + x(51) + x(53)-15;
        x(55) + x(57) + x(59) + x(50) + x(52)+ x(54)-15;
        x(56) + x(58) + x(60)-15; 
        x(61) + x(63) + x(65)-15;
        x(67) + x(69) + x(71) + x(62) + x(64)+ x(66)-15;
        x(68) + x(70) + x(72)-15; 
        x(1)+x(2)+ x(13)+x(14)+x(25)+x(26)+ x(37)+x(38)+ x(49)+x(50)+ x(61)+x(62)-dA1;
        x(7)+x(8)+ x(19)+x(20)+x(31)+x(32)+ x(43)+x(44)+ x(55)+x(56)+ x(67)+x(68)-dA2;
        x(3)+x(4)+ x(15)+x(16)+x(27)+x(28)+ x(39)+x(40)+ x(51)+x(52)+ x(63)+x(64)-dB1;
        x(9)+x(10)+ x(21)+x(22)+x(33)+x(34)+ x(45)+x(46)+ x(57)+x(58)+ x(69)+x(70)-dB2 ];

   % Nonlinear equality constraints
  ceq = [];

function f = objfun(x)
f = (339*x(1)*x(2))/6050 + (68*x(7)*x(8))/3969 + (339*x(1)*x(13))/6050 + (339*x(1)*x(14))/6050 + (339*x(2)*x(13))/6050 + (339*x(2)*x(14))/6050 + (68*x(7)*x(19))/3969 + (68*x(7)*x(8))/3969 + (68*x(8)*x(19))/3969 + (68*x(8)*x(20))/3969 + (339*x(1)*x(25))/6050 + (339*x(1)*x(26))/6050 + (339*x(2)*x(25))/6050 + (339*x(13)*x(14))/6050 + (339*x(2)*x(26))/6050 + (68*x(7)*x(31))/3969 + (68*x(7)*x(32))/3969 + (68*x(8)*x(31))/3969 + (68*x(19)*x(20))/3969 + (68*x(8)*x(32))/3969 - (159*x(1)*x(3))/8470 - (159*x(1)*x(4))/8470 - (159*x(2)*x(3))/8470 - (159*x(2)*x(4))/8470 - (2*x(7)*x(9))/189 - (2*x(7)*x(10))/189 - (2*x(8)*x(9))/189 - (2*x(8)*x(10))/189 + (339*x(1)*x(37))/6050 + (339*x(13)*x(25))/6050 + (339*x(1)*x(38))/6050 + (339*x(2)*x(37))/6050 + (339*x(13)*x(26))/6050 + (339*x(14)*x(25))/6050 + (339*x(2)*x(38))/6050 + (339*x(14)*x(26))/6050 + (68*x(7)*x(43))/3969 + (68*x(19)*x(31))/3969 + (68*x(7)*x(44))/3969 + (68*x(8)*x(43))/3969 + (68*x(19)*x(32))/3969 + (68*x(20)*x(31))/3969 + (68*x(8)*x(44))/3969 + (68*x(20)*x(32))/3969 - (159*x(1)*x(15))/8470 - (159*x(13)*x(3))/8470 - (159*x(1)*x(16))/8470 - (159*x(2)*x(15))/8470 - (159*x(13)*x(4))/8470 - (159*x(14)*x(3))/8470 - (159*x(2)*x(16))/8470 - (159*x(14)*x(4))/8470 - (2*x(7)*x(21))/189 - (2*x(19)*x(9))/189 - (2*x(7)*x(22))/189 - (2*x(8)*x(21))/189 - (2*x(19)*x(10))/189 - (2*x(20)*x(9))/189 - (2*x(8)*x(22))/189 - (2*x(20)*x(10))/189 + (339*x(1)*x(49))/6050 + (339*x(13)*x(37))/6050 + (339*x(1)*x(50))/6050 + (339*x(2)*x(49))/6050 + (339*x(13)*x(38))/6050 + (339*x(14)*x(37))/6050 + (339*x(25)*x(26))/6050 + (339*x(2)*x(50))/6050 + (339*x(14)*x(38))/6050 + (68*x(7)*x(55))/3969 + (68*x(19)*x(43))/3969 + (68*x(7)*x(56))/3969 + (68*x(8)*x(55))/3969 + (68*x(19)*x(44))/3969 + (68*x(20)*x(43))/3969 + (68*x(31)*x(32))/3969 + (68*x(8)*x(56))/3969 + (68*x(20)*x(44))/3969 - (159*x(1)*x(27))/8470 - (159*x(13)*x(15))/8470 - (159*x(25)*x(3))/8470 - (159*x(1)*x(28))/8470 - (159*x(2)*x(27))/8470 - (159*x(13)*x(16))/8470 - (159*x(14)*x(15))/8470 - (159*x(25)*x(4))/8470 - (159*x(26)*x(3))/8470 - (159*x(2)*x(28))/8470 - (159*x(14)*x(16))/8470 - (159*x(26)*x(4))/8470 - (2*x(7)*x(33))/189 - (2*x(19)*x(21))/189 - (2*x(31)*x(9))/189 - (2*x(7)*x(34))/189 - (2*x(8)*x(33))/189 - (2*x(19)*x(22))/189 - (2*x(20)*x(21))/189 - (2*x(31)*x(10))/189 - (2*x(32)*x(9))/189 - (2*x(8)*x(34))/189 - (2*x(20)*x(22))/189 - (2*x(32)*x(10))/189 + (339*x(1)*x(61))/6050 + (339*x(13)*x(49))/6050 + (339*x(25)*x(37))/6050 + (339*x(1)*x(62))/6050 + (339*x(2)*x(61))/6050 + (339*x(13)*x(50))/6050 + (339*x(14)*x(49))/6050 + (339*x(25)*x(38))/6050 + (339*x(26)*x(37))/6050 - (9*x(1)*x(5))/605 + (339*x(2)*x(62))/6050 + (339*x(14)*x(50))/6050 + (339*x(26)*x(38))/6050 - (9*x(1)*x(6))/605 - (9*x(2)*x(5))/605 + (68*x(7)*x(67))/3969 + (68*x(19)*x(55))/3969 + (68*x(31)*x(43))/3969 + (323*x(3)*x(4))/11858 - (9*x(2)*x(6))/605 + (68*x(7)*x(68))/3969 + (68*x(8)*x(67))/3969 + (68*x(19)*x(56))/3969 + (68*x(20)*x(55))/3969 + (68*x(31)*x(44))/3969 + (68*x(32)*x(43))/3969 - (106*x(7)*x(11))/6615 + (68*x(8)*x(68))/3969 + (68*x(20)*x(56))/3969 + (68*x(32)*x(44))/3969 - (106*x(7)*x(12))/6615 - (106*x(8)*x(11))/6615 + (4*x(9)*x(10))/147 - (106*x(8)*x(12))/6615 - (159*x(1)*x(39))/8470 - (159*x(13)*x(27))/8470 - (159*x(25)*x(15))/8470 - (159*x(3)*x(37))/8470 - (159*x(1)*x(40))/8470 - (159*x(2)*x(39))/8470 - (159*x(13)*x(28))/8470 - (159*x(14)*x(27))/8470 - (159*x(25)*x(16))/8470 - (159*x(26)*x(15))/8470 - (159*x(3)*x(38))/8470 - (159*x(4)*x(37))/8470 - (159*x(2)*x(40))/8470 - (159*x(14)*x(28))/8470 - (159*x(26)*x(16))/8470 - (159*x(4)*x(38))/8470 - (2*x(7)*x(45))/189 - (2*x(19)*x(33))/189 - (2*x(31)*x(21))/189 - (2*x(9)*x(43))/189 - (2*x(7)*x(46))/189 - (2*x(8)*x(45))/189 - (2*x(19)*x(34))/189 - (2*x(20)*x(33))/189 - (2*x(31)*x(22))/189 - (2*x(32)*x(21))/189 - (2*x(9)*x(44))/189 - (2*x(10)*x(43))/189 - (2*x(8)*x(46))/189 - (2*x(20)*x(34))/189 - (2*x(32)*x(22))/189 - (2*x(10)*x(44))/189 + (339*x(13)*x(61))/6050 + (339*x(25)*x(49))/6050 + (339*x(13)*x(62))/6050 + (339*x(14)*x(61))/6050 + (339*x(25)*x(50))/6050 + (339*x(26)*x(49))/6050 + (339*x(37)*x(38))/6050 - (9*x(1)*x(17))/605 - (9*x(13)*x(5))/605 + (323*x(3)*x(15))/11858 + (339*x(14)*x(62))/6050 + (339*x(26)*x(50))/6050 - (9*x(1)*x(18))/605 - (9*x(2)*x(17))/605 - (9*x(13)*x(6))/605 - (9*x(14)*x(5))/605 + (68*x(19)*x(67))/3969 + (68*x(31)*x(55))/3969 + (323*x(3)*x(16))/11858 + (323*x(4)*x(15))/11858 - (9*x(2)*x(18))/605 - (9*x(14)*x(6))/605 + (68*x(19)*x(68))/3969 + (68*x(20)*x(67))/3969 + (68*x(31)*x(56))/3969 + (68*x(32)*x(55))/3969 + (323*x(4)*x(16))/11858 + (68*x(43)*x(44))/3969 - (106*x(7)*x(23))/6615 - (106*x(19)*x(11))/6615 + (4*x(9)*x(21))/147 + (68*x(20)*x(68))/3969 + (68*x(32)*x(56))/3969 - (106*x(7)*x(24))/6615 - (106*x(8)*x(23))/6615 - (106*x(19)*x(12))/6615 - (106*x(20)*x(11))/6615 + (4*x(9)*x(22))/147 + (4*x(10)*x(21))/147 - (106*x(8)*x(24))/6615 - (106*x(20)*x(12))/6615 + (4*x(10)*x(22))/147 - (159*x(1)*x(51))/8470 - (159*x(13)*x(39))/8470 - (159*x(25)*x(27))/8470 - (159*x(3)*x(49))/8470 - (159*x(37)*x(15))/8470 - (159*x(1)*x(52))/8470 - (159*x(2)*x(51))/8470 - (159*x(13)*x(40))/8470 - (159*x(14)*x(39))/8470 - (159*x(25)*x(28))/8470 - (159*x(26)*x(27))/8470 - (159*x(3)*x(50))/8470 - (159*x(4)*x(49))/8470 - (159*x(37)*x(16))/8470 - (159*x(38)*x(15))/8470 - (159*x(2)*x(52))/8470 - (159*x(14)*x(40))/8470 - (159*x(26)*x(28))/8470 - (159*x(4)*x(50))/8470 - (159*x(38)*x(16))/8470 - (2*x(7)*x(57))/189 - (2*x(19)*x(45))/189 - (2*x(31)*x(33))/189 - (2*x(9)*x(55))/189 - (2*x(43)*x(21))/189 - (2*x(7)*x(58))/189 - (2*x(8)*x(57))/189 - (2*x(19)*x(46))/189 - (2*x(20)*x(45))/189 - (2*x(31)*x(34))/189 - (2*x(32)*x(33))/189 - (2*x(9)*x(56))/189 - (2*x(10)*x(55))/189 - (2*x(43)*x(22))/189 - (2*x(44)*x(21))/189 - (2*x(8)*x(58))/189 - (2*x(20)*x(46))/189 - (2*x(32)*x(34))/189 - (2*x(10)*x(56))/189 - (2*x(44)*x(22))/189 + (339*x(25)*x(61))/6050 + (339*x(37)*x(49))/6050 + (339*x(25)*x(62))/6050 + (339*x(26)*x(61))/6050 + (339*x(37)*x(50))/6050 + (339*x(38)*x(49))/6050 - (9*x(1)*x(29))/605 - (9*x(13)*x(17))/605 - (9*x(25)*x(5))/605 + (323*x(3)*x(27))/11858 + (339*x(26)*x(62))/6050 + (339*x(38)*x(50))/6050 - (9*x(1)*x(30))/605 - (9*x(2)*x(29))/605 - (9*x(13)*x(18))/605 - (9*x(14)*x(17))/605 - (9*x(25)*x(6))/605 - (9*x(26)*x(5))/605 + (68*x(31)*x(67))/3969 + (323*x(3)*x(28))/11858 + (323*x(4)*x(27))/11858 + (68*x(43)*x(55))/3969 + (323*x(15)*x(16))/11858 - (9*x(2)*x(30))/605 - (9*x(14)*x(18))/605 - (9*x(26)*x(6))/605 + (68*x(31)*x(68))/3969 + (68*x(32)*x(67))/3969 + (323*x(4)*x(28))/11858 + (68*x(43)*x(56))/3969 + (68*x(44)*x(55))/3969 - (106*x(7)*x(35))/6615 - (106*x(19)*x(23))/6615 - (106*x(31)*x(11))/6615 + (4*x(9)*x(33))/147 + (68*x(32)*x(68))/3969 + (68*x(44)*x(56))/3969 - (106*x(7)*x(36))/6615 - (106*x(8)*x(35))/6615 - (106*x(19)*x(24))/6615 - (106*x(20)*x(23))/6615 - (106*x(31)*x(12))/6615 - (106*x(32)*x(11))/6615 + (4*x(9)*x(34))/147 + (4*x(10)*x(33))/147 + (4*x(21)*x(22))/147 - (106*x(8)*x(36))/6615 - (106*x(20)*x(24))/6615 - (106*x(32)*x(12))/6615 + (4*x(10)*x(34))/147 - (159*x(1)*x(63))/8470 - (159*x(13)*x(51))/8470 - (159*x(25)*x(39))/8470 - (159*x(3)*x(61))/8470 - (159*x(37)*x(27))/8470 - (159*x(15)*x(49))/8470 - (159*x(1)*x(64))/8470 - (159*x(2)*x(63))/8470 - (159*x(13)*x(52))/8470 - (159*x(14)*x(51))/8470 - (159*x(25)*x(40))/8470 - (159*x(26)*x(39))/8470 - (159*x(3)*x(62))/8470 - (159*x(4)*x(61))/8470 - (159*x(37)*x(28))/8470 - (159*x(38)*x(27))/8470 - (159*x(15)*x(50))/8470 - (159*x(16)*x(49))/8470 - (41*x(3)*x(5))/4235 - (159*x(2)*x(64))/8470 - (159*x(14)*x(52))/8470 - (159*x(26)*x(40))/8470 - (159*x(4)*x(62))/8470 - (159*x(38)*x(28))/8470 - (159*x(16)*x(50))/8470 - (2*x(7)*x(69))/189 - (2*x(19)*x(57))/189 - (2*x(31)*x(45))/189 - (41*x(3)*x(6))/4235 - (41*x(4)*x(5))/4235 - (2*x(9)*x(67))/189 - (2*x(43)*x(33))/189 - (2*x(21)*x(55))/189 - (2*x(7)*x(70))/189 - (2*x(8)*x(69))/189 - (2*x(19)*x(58))/189 - (2*x(20)*x(57))/189 - (2*x(31)*x(46))/189 - (2*x(32)*x(45))/189 - (41*x(4)*x(6))/4235 - (2*x(9)*x(68))/189 - (2*x(10)*x(67))/189 - (2*x(43)*x(34))/189 - (2*x(44)*x(33))/189 - (2*x(21)*x(56))/189 - (2*x(22)*x(55))/189 - (2*x(9)*x(11))/105 - (2*x(8)*x(70))/189 - (2*x(20)*x(58))/189 - (2*x(32)*x(46))/189 - (2*x(10)*x(68))/189 - (2*x(44)*x(34))/189 - (2*x(22)*x(56))/189 - (2*x(9)*x(12))/105 - (2*x(10)*x(11))/105 + (339*x(37)*x(61))/6050 - (2*x(10)*x(12))/105 + (339*x(37)*x(62))/6050 + (339*x(38)*x(61))/6050 + (339*x(49)*x(50))/6050 - (9*x(1)*x(41))/605 - (9*x(13)*x(29))/605 - (9*x(25)*x(17))/605 + (323*x(3)*x(39))/11858 - (9*x(37)*x(5))/605 + (323*x(15)*x(27))/11858 + (339*x(38)*x(62))/6050 - (9*x(1)*x(42))/605 - (9*x(2)*x(41))/605 - (9*x(13)*x(30))/605 - (9*x(14)*x(29))/605 - (9*x(25)*x(18))/605 - (9*x(26)*x(17))/605 + (323*x(3)*x(40))/11858 + (323*x(4)*x(39))/11858 - (9*x(37)*x(6))/605 - (9*x(38)*x(5))/605 + (68*x(43)*x(67))/3969 + (323*x(15)*x(28))/11858 + (323*x(16)*x(27))/11858 - (9*x(2)*x(42))/605 - (9*x(14)*x(30))/605 - (9*x(26)*x(18))/605 + (323*x(4)*x(40))/11858 - (9*x(38)*x(6))/605 + (68*x(43)*x(68))/3969 + (68*x(44)*x(67))/3969 + (323*x(16)*x(28))/11858 + (68*x(55)*x(56))/3969 - (106*x(7)*x(47))/6615 - (106*x(19)*x(35))/6615 - (106*x(31)*x(23))/6615 + (4*x(9)*x(45))/147 - (106*x(43)*x(11))/6615 + (4*x(21)*x(33))/147 + (68*x(44)*x(68))/3969 - (106*x(7)*x(48))/6615 - (106*x(8)*x(47))/6615 - (106*x(19)*x(36))/6615 - (106*x(20)*x(35))/6615 - (106*x(31)*x(24))/6615 - (106*x(32)*x(23))/6615 + (4*x(9)*x(46))/147 + (4*x(10)*x(45))/147 - (106*x(43)*x(12))/6615 - (106*x(44)*x(11))/6615 + (4*x(21)*x(34))/147 + (4*x(22)*x(33))/147 - (106*x(8)*x(48))/6615 - (106*x(20)*x(36))/6615 - (106*x(32)*x(24))/6615 + (4*x(10)*x(46))/147 - (106*x(44)*x(12))/6615 + (4*x(22)*x(34))/147 - (159*x(13)*x(63))/8470 - (159*x(25)*x(51))/8470 - (159*x(37)*x(39))/8470 - (159*x(15)*x(61))/8470 - (159*x(49)*x(27))/8470 - (159*x(13)*x(64))/8470 - (159*x(14)*x(63))/8470 - (159*x(25)*x(52))/8470 - (159*x(26)*x(51))/8470 - (159*x(37)*x(40))/8470 - (159*x(38)*x(39))/8470 - (159*x(15)*x(62))/8470 - (159*x(16)*x(61))/8470 - (159*x(49)*x(28))/8470 - (159*x(50)*x(27))/8470 - (41*x(3)*x(17))/4235 - (41*x(15)*x(5))/4235 - (159*x(14)*x(64))/8470 - (159*x(26)*x(52))/8470 - (159*x(38)*x(40))/8470 - (159*x(16)*x(62))/8470 - 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(41*x(16)*x(53))/4235 - (41*x(27)*x(42))/4235 - (41*x(28)*x(41))/4235 - (2*x(67)*x(69))/189 - (41*x(5)*x(64))/4235 - (41*x(6)*x(63))/4235 - (41*x(39)*x(30))/4235 - (41*x(40)*x(29))/4235 - (41*x(17)*x(52))/4235 - (41*x(18)*x(51))/4235 - (41*x(4)*x(66))/4235 - (41*x(16)*x(54))/4235 - (41*x(28)*x(42))/4235 - (2*x(67)*x(70))/189 - (2*x(68)*x(69))/189 - (41*x(6)*x(64))/4235 - (41*x(40)*x(30))/4235 - (41*x(18)*x(52))/4235 - (2*x(9)*x(71))/105 - (2*x(21)*x(59))/105 - (2*x(33)*x(47))/105 - (2*x(11)*x(69))/105 - (2*x(45)*x(35))/105 - (2*x(23)*x(57))/105 - (2*x(68)*x(70))/189 - (2*x(9)*x(72))/105 - (2*x(10)*x(71))/105 - (2*x(21)*x(60))/105 - (2*x(22)*x(59))/105 - (2*x(33)*x(48))/105 - (2*x(34)*x(47))/105 - (2*x(11)*x(70))/105 - (2*x(12)*x(69))/105 - (2*x(45)*x(36))/105 - (2*x(46)*x(35))/105 - (2*x(23)*x(58))/105 - (2*x(24)*x(57))/105 - (2*x(10)*x(72))/105 - (2*x(22)*x(60))/105 - (2*x(34)*x(48))/105 - (2*x(12)*x(70))/105 - (2*x(46)*x(36))/105 - (2*x(24)*x(58))/105 - (9*x(37)*x(65))/605 - (9*x(49)*x(53))/605 - (9*x(61)*x(41))/605 + (323*x(39)*x(63))/11858 - (9*x(37)*x(66))/605 - (9*x(38)*x(65))/605 - (9*x(49)*x(54))/605 - (9*x(50)*x(53))/605 - (9*x(61)*x(42))/605 - (9*x(62)*x(41))/605 + (323*x(39)*x(64))/11858 + (323*x(40)*x(63))/11858 + (323*x(51)*x(52))/11858 + (43*x(5)*x(41))/3025 + (43*x(17)*x(29))/3025 - (9*x(38)*x(66))/605 - (9*x(50)*x(54))/605 - (9*x(62)*x(42))/605 + (323*x(40)*x(64))/11858 - (106*x(43)*x(71))/6615 - (106*x(55)*x(59))/6615 - (106*x(67)*x(47))/6615 + (43*x(5)*x(42))/3025 + (43*x(6)*x(41))/3025 + (4*x(45)*x(69))/147 + (43*x(17)*x(30))/3025 + (43*x(18)*x(29))/3025 - (106*x(43)*x(72))/6615 - (106*x(44)*x(71))/6615 - (106*x(55)*x(60))/6615 - (106*x(56)*x(59))/6615 - (106*x(67)*x(48))/6615 - (106*x(68)*x(47))/6615 + (43*x(6)*x(42))/3025 + (4*x(45)*x(70))/147 + (4*x(46)*x(69))/147 + (43*x(18)*x(30))/3025 + (4*x(57)*x(58))/147 + (68*x(11)*x(47))/1225 + (68*x(23)*x(35))/1225 - (106*x(44)*x(72))/6615 - (106*x(56)*x(60))/6615 - (106*x(68)*x(48))/6615 + (4*x(46)*x(70))/147 + (68*x(11)*x(48))/1225 + (68*x(12)*x(47))/1225 + (68*x(23)*x(36))/1225 + (68*x(24)*x(35))/1225 + (68*x(12)*x(48))/1225 + (68*x(24)*x(36))/1225 - (41*x(15)*x(65))/4235 - (41*x(27)*x(53))/4235 - (41*x(39)*x(41))/4235 - (41*x(17)*x(63))/4235 - (41*x(51)*x(29))/4235 - (41*x(15)*x(66))/4235 - (41*x(16)*x(65))/4235 - (41*x(27)*x(54))/4235 - (41*x(28)*x(53))/4235 - (41*x(39)*x(42))/4235 - (41*x(40)*x(41))/4235 - (41*x(17)*x(64))/4235 - (41*x(18)*x(63))/4235 - (41*x(51)*x(30))/4235 - (41*x(52)*x(29))/4235 - (41*x(16)*x(66))/4235 - (41*x(28)*x(54))/4235 - (41*x(40)*x(42))/4235 - (41*x(18)*x(64))/4235 - (41*x(52)*x(30))/4235 - (2*x(21)*x(71))/105 - (2*x(33)*x(59))/105 - (2*x(45)*x(47))/105 - (2*x(23)*x(69))/105 - (2*x(57)*x(35))/105 - (2*x(21)*x(72))/105 - (2*x(22)*x(71))/105 - (2*x(33)*x(60))/105 - (2*x(34)*x(59))/105 - (2*x(45)*x(48))/105 - (2*x(46)*x(47))/105 - (2*x(23)*x(70))/105 - (2*x(24)*x(69))/105 - (2*x(57)*x(36))/105 - (2*x(58)*x(35))/105 - (2*x(22)*x(72))/105 - (2*x(34)*x(60))/105 - (2*x(46)*x(48))/105 - (2*x(24)*x(70))/105 - (2*x(58)*x(36))/105 - (9*x(49)*x(65))/605 - (9*x(61)*x(53))/605 + (323*x(51)*x(63))/11858 - (9*x(49)*x(66))/605 - (9*x(50)*x(65))/605 - (9*x(61)*x(54))/605 - (9*x(62)*x(53))/605 + (323*x(51)*x(64))/11858 + (323*x(52)*x(63))/11858 + (43*x(5)*x(53))/3025 + (43*x(17)*x(41))/3025 - (9*x(50)*x(66))/605 - (9*x(62)*x(54))/605 + (323*x(52)*x(64))/11858 - (106*x(55)*x(71))/6615 - (106*x(67)*x(59))/6615 + (43*x(5)*x(54))/3025 + (43*x(6)*x(53))/3025 + (43*x(17)*x(42))/3025 + (43*x(18)*x(41))/3025 + (4*x(57)*x(69))/147 + (43*x(29)*x(30))/3025 - (106*x(55)*x(72))/6615 - (106*x(56)*x(71))/6615 - (106*x(67)*x(60))/6615 - (106*x(68)*x(59))/6615 + (43*x(6)*x(54))/3025 + (43*x(18)*x(42))/3025 + (4*x(57)*x(70))/147 + (4*x(58)*x(69))/147 + (68*x(11)*x(59))/1225 + (68*x(23)*x(47))/1225 - (106*x(56)*x(72))/6615 - (106*x(68)*x(60))/6615 + (4*x(58)*x(70))/147 + (68*x(11)*x(60))/1225 + (68*x(12)*x(59))/1225 + (68*x(23)*x(48))/1225 + (68*x(24)*x(47))/1225 + (68*x(35)*x(36))/1225 + (68*x(12)*x(60))/1225 + (68*x(24)*x(48))/1225 - (41*x(27)*x(65))/4235 - (41*x(39)*x(53))/4235 - (41*x(51)*x(41))/4235 - (41*x(29)*x(63))/4235 - (41*x(27)*x(66))/4235 - (41*x(28)*x(65))/4235 - (41*x(39)*x(54))/4235 - (41*x(40)*x(53))/4235 - (41*x(51)*x(42))/4235 - (41*x(52)*x(41))/4235 - (41*x(29)*x(64))/4235 - (41*x(30)*x(63))/4235 - (41*x(28)*x(66))/4235 - (41*x(40)*x(54))/4235 - (41*x(52)*x(42))/4235 - (41*x(30)*x(64))/4235 - (2*x(33)*x(71))/105 - (2*x(45)*x(59))/105 - (2*x(57)*x(47))/105 - (2*x(35)*x(69))/105 - (2*x(33)*x(72))/105 - (2*x(34)*x(71))/105 - (2*x(45)*x(60))/105 - (2*x(46)*x(59))/105 - (2*x(57)*x(48))/105 - (2*x(58)*x(47))/105 - (2*x(35)*x(70))/105 - (2*x(36)*x(69))/105 - (2*x(34)*x(72))/105 - (2*x(46)*x(60))/105 - (2*x(58)*x(48))/105 - (2*x(36)*x(70))/105 - (9*x(61)*x(65))/605 - (9*x(61)*x(66))/605 - (9*x(62)*x(65))/605 + (323*x(63)*x(64))/11858 + (43*x(5)*x(65))/3025 + (43*x(17)*x(53))/3025 + (43*x(29)*x(41))/3025 - (9*x(62)*x(66))/605 - (106*x(67)*x(71))/6615 + (43*x(5)*x(66))/3025 + (43*x(6)*x(65))/3025 + (43*x(17)*x(54))/3025 + (43*x(18)*x(53))/3025 + (43*x(29)*x(42))/3025 + (43*x(30)*x(41))/3025 - (106*x(67)*x(72))/6615 - (106*x(68)*x(71))/6615 + (43*x(6)*x(66))/3025 + (43*x(18)*x(54))/3025 + (43*x(30)*x(42))/3025 + (4*x(69)*x(70))/147 + (68*x(11)*x(71))/1225 + (68*x(23)*x(59))/1225 + (68*x(35)*x(47))/1225 - (106*x(68)*x(72))/6615 + (68*x(11)*x(72))/1225 + (68*x(12)*x(71))/1225 + (68*x(23)*x(60))/1225 + (68*x(24)*x(59))/1225 + (68*x(35)*x(48))/1225 + (68*x(36)*x(47))/1225 + (68*x(12)*x(72))/1225 + (68*x(24)*x(60))/1225 + (68*x(36)*x(48))/1225 - (41*x(39)*x(65))/4235 - (41*x(51)*x(53))/4235 - (41*x(63)*x(41))/4235 - (41*x(39)*x(66))/4235 - (41*x(40)*x(65))/4235 - (41*x(51)*x(54))/4235 - (41*x(52)*x(53))/4235 - (41*x(63)*x(42))/4235 - (41*x(64)*x(41))/4235 - (41*x(40)*x(66))/4235 - (41*x(52)*x(54))/4235 - (41*x(64)*x(42))/4235 - (2*x(45)*x(71))/105 - (2*x(57)*x(59))/105 - (2*x(69)*x(47))/105 - (2*x(45)*x(72))/105 - (2*x(46)*x(71))/105 - (2*x(57)*x(60))/105 - (2*x(58)*x(59))/105 - (2*x(69)*x(48))/105 - (2*x(70)*x(47))/105 - (2*x(46)*x(72))/105 - (2*x(58)*x(60))/105 - (2*x(70)*x(48))/105 + (43*x(17)*x(65))/3025 + (43*x(29)*x(53))/3025 + (43*x(17)*x(66))/3025 + (43*x(18)*x(65))/3025 + (43*x(29)*x(54))/3025 + (43*x(30)*x(53))/3025 + (43*x(41)*x(42))/3025 + (43*x(18)*x(66))/3025 + (43*x(30)*x(54))/3025 + (68*x(23)*x(71))/1225 + (68*x(35)*x(59))/1225 + (68*x(23)*x(72))/1225 + (68*x(24)*x(71))/1225 + (68*x(35)*x(60))/1225 + (68*x(36)*x(59))/1225 + (68*x(47)*x(48))/1225 + (68*x(24)*x(72))/1225 + (68*x(36)*x(60))/1225 - (41*x(51)*x(65))/4235 - (41*x(63)*x(53))/4235 - (41*x(51)*x(66))/4235 - (41*x(52)*x(65))/4235 - (41*x(63)*x(54))/4235 - (41*x(64)*x(53))/4235 - (41*x(52)*x(66))/4235 - (41*x(64)*x(54))/4235 - (2*x(57)*x(71))/105 - (2*x(69)*x(59))/105 - (2*x(57)*x(72))/105 - (2*x(58)*x(71))/105 - (2*x(69)*x(60))/105 - (2*x(70)*x(59))/105 - (2*x(58)*x(72))/105 - (2*x(70)*x(60))/105 + (43*x(29)*x(65))/3025 + (43*x(41)*x(53))/3025 + (43*x(29)*x(66))/3025 + (43*x(30)*x(65))/3025 + (43*x(41)*x(54))/3025 + (43*x(42)*x(53))/3025 + (43*x(30)*x(66))/3025 + (43*x(42)*x(54))/3025 + (68*x(35)*x(71))/1225 + (68*x(47)*x(59))/1225 + (68*x(35)*x(72))/1225 + (68*x(36)*x(71))/1225 + (68*x(47)*x(60))/1225 + (68*x(48)*x(59))/1225 + (68*x(36)*x(72))/1225 + (68*x(48)*x(60))/1225 - (41*x(63)*x(65))/4235 - (41*x(63)*x(66))/4235 - (41*x(64)*x(65))/4235 - (41*x(64)*x(66))/4235 - (2*x(69)*x(71))/105 - (2*x(69)*x(72))/105 - (2*x(70)*x(71))/105 - (2*x(70)*x(72))/105 + (43*x(41)*x(65))/3025 + (43*x(41)*x(66))/3025 + (43*x(42)*x(65))/3025 + (43*x(53)*x(54))/3025 + (43*x(42)*x(66))/3025 + (68*x(47)*x(71))/1225 + (68*x(47)*x(72))/1225 + (68*x(48)*x(71))/1225 + (68*x(59)*x(60))/1225 + (68*x(48)*x(72))/1225 + (43*x(53)*x(65))/3025 + (43*x(53)*x(66))/3025 + (43*x(54)*x(65))/3025 + (43*x(54)*x(66))/3025 + (68*x(59)*x(71))/1225 + (68*x(59)*x(72))/1225 + (68*x(60)*x(71))/1225 + (68*x(60)*x(72))/1225 + (43*x(65)*x(66))/3025 + (68*x(71)*x(72))/1225 + (339*x(1)^2)/12100 + (339*x(2)^2)/12100 + (34*x(7)^2)/3969 + (34*x(8)^2)/3969 + (339*x(13)^2)/12100 + (339*x(14)^2)/12100 + (34*x(19)^2)/3969 + (34*x(20)^2)/3969 + (339*x(25)^2)/12100 + (339*x(26)^2)/12100 + (34*x(31)^2)/3969 + (34*x(32)^2)/3969 + (323*x(3)^2)/23716 + (323*x(4)^2)/23716 + (2*x(9)^2)/147 + (2*x(10)^2)/147 + (339*x(37)^2)/12100 + (339*x(38)^2)/12100 + (34*x(43)^2)/3969 + (34*x(44)^2)/3969 + (323*x(15)^2)/23716 + (323*x(16)^2)/23716 + (2*x(21)^2)/147 + (2*x(22)^2)/147 + (339*x(49)^2)/12100 + (339*x(50)^2)/12100 + (34*x(55)^2)/3969 + (34*x(56)^2)/3969 + (323*x(27)^2)/23716 + (323*x(28)^2)/23716 + (2*x(33)^2)/147 + (2*x(34)^2)/147 + (339*x(61)^2)/12100 + (339*x(62)^2)/12100 + (34*x(67)^2)/3969 + (43*x(5)^2)/6050 + (34*x(68)^2)/3969 + (43*x(6)^2)/6050 + (34*x(11)^2)/1225 + (34*x(12)^2)/1225 + (323*x(39)^2)/23716 + (323*x(40)^2)/23716 + (2*x(45)^2)/147 + (2*x(46)^2)/147 + (43*x(17)^2)/6050 + (43*x(18)^2)/6050 + (34*x(23)^2)/1225 + (34*x(24)^2)/1225 + (323*x(51)^2)/23716 + (323*x(52)^2)/23716 + (2*x(57)^2)/147 + (2*x(58)^2)/147 + (43*x(29)^2)/6050 + (43*x(30)^2)/6050 + (34*x(35)^2)/1225 + (34*x(36)^2)/1225 + (323*x(63)^2)/23716 + (323*x(64)^2)/23716 + (2*x(69)^2)/147 + (2*x(70)^2)/147 + (43*x(41)^2)/6050 + (43*x(42)^2)/6050 + (34*x(47)^2)/1225 + (34*x(48)^2)/1225 + (43*x(53)^2)/6050 + (43*x(54)^2)/6050 + (34*x(59)^2)/1225 + (34*x(60)^2)/1225 + (43*x(65)^2)/6050 + (43*x(66)^2)/6050 + (34*x(71)^2)/1225 + (34*x(72)^2)/1225;

clc;
clear;
close all;
ub = [Inf;Inf;Inf; Inf;Inf;Inf; Inf;Inf;Inf; Inf;Inf;Inf; 
Inf;Inf;Inf; Inf;Inf;Inf; Inf;Inf;Inf; Inf;Inf;Inf;
Inf;Inf;Inf; Inf;Inf;Inf; Inf;Inf;Inf; Inf;Inf;Inf;
Inf;Inf;Inf; Inf;Inf;Inf; Inf;Inf;Inf; Inf;Inf;Inf; 
Inf;Inf;Inf; Inf;Inf;Inf; Inf;Inf;Inf; Inf;Inf;Inf;
Inf;Inf;Inf; Inf;Inf;Inf; Inf;Inf;Inf; Inf;Inf;Inf;
1;1;1; 1;1;1; 1;1;1; 1;1;1; 1;1;1; 1;1;1];   
x0 = ones(90,1);     
options = optimset('Algorithm','active-set');
%options = optimoptions(@fmincon,'Algorithm','sqp');
[x,fval] = fmincon(@objfun,x0,[],[],[],[],[],ub,@confun,options);

I'm not sure if I can use binary and continuous variables in fmincon function. How can I incorporate binary variables? Note that constraints are linear. Any help would be extremely appreciated.

Answer 1

[Matt J]

No, fmincon is only for smooth, continuous optimization problems. Since your objective is nonlinear, you will have to use ga(). (If the objective were linear, you could use intlinprog).

Before using GA, though, it might be helpful to first solve the problem with fmincon without binary constraints on x(73)-x(90). Then use that result as part of the starting population for ga(), rounding the initial x(73)-x(90) values to binary ones.

Incidentally, because your constraints are linear, it is probably not a good idea to pretend they are non-linear, as you are doing currently by implementing them through confun(). Similarly, since your objective function looks quadratic, solving a continuous approximation of the problem is probably best done using QUADPROG rather than FMINCON.

[rezi raf]

thank you @Matt J.. I solved the problem by Quadprog and I obtained the value of x(i), i=1..90. The problem is that each binary variables takes the value 0.2. For instance, according to constraint 1 only two of the x(73),x(74),x(75),x(76),x(77) and x(78)variables should be equal to 1; otherwise, the results do not make sense. I need to find an optimal solution for the problem. Even I used GA to solve this problem but the quality of solutions were poor.

[Matt J]

Even I used GA to solve this problem but the quality of solutions were poor.

My intention was that you use them both - use fmincon to solve in fully continuous space and then initialize GA (binary constrained) with the fmincon solution.