For routines that permit equality constraints, nonlinear equality constraints must be computed with the nonlinear inequality constraints. For linear equalities, the coefficients of the equalities are passed in through the matrix Aeq and the right-hand-side vector beq.
For example, if you have the nonlinear equality constraint and the nonlinear inequality constraint x1x2 ≥ –10, rewrite them as
and then solve the problem using the following steps.
function f = objfun(x) f = exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1);
function [c, ceq] = confuneq(x) % Nonlinear inequality constraints c = -x(1)*x(2) - 10; % Nonlinear equality constraints ceq = x(1)^2 + x(2) - 1;
x0 = [-1,1]; % Make a starting guess at the solution options = optimoptions(@fmincon,'Algorithm','sqp'); [x,fval] = fmincon(@objfun,x0,,,,,,,... @confuneq,options);
After 21 function evaluations, the solution produced is
x,fval x = -0.7529 0.4332 fval = 1.5093 [c,ceq] = confuneq(x) % Check the constraint values at x c = -9.6739 ceq = 5.3291e-15
Note that ceq is equal to 0 within the default tolerance on the constraints of 1.0e-006 and that c is less than or equal to 0, as desired.