I am facing a problem in the estimation of variables from the multivariable mathematical equations. The variables (t,tf,w1,w2) that I am trying to minimize are exist in both the equality and inequality constraints. In the following equations q1 and q2 are any numeric values and t is a continuous varaiable.
minimize tf,w1,w2 subjected to:
(1) tf≥0
(2) 0≤t≤tf
(3)-((w1/(2*tf))*(tf-t(i))^2)+(w2/(2*tf))*(t(i))^2+ (q2/tf - tf*w2/6)- (q1/tf - tf*w1/6)≤370
(4) [(w1/h)*(tf-t)+(w2/h)*(t)]≤140;
(5) (w2-w1/tf)≤300;
(6) -((w1*tf)/2)+(q2-q1)/tf+((w1-w2)*tf/6)=0;
(7) ((w2*tf)/2)+(q2-q1)/tf+((w1-w2)*tf/6)=0;
I have already tried to solve the problem through fmincon in Matlab but unable to get a feasible solution. options = optimoptions(@fmincon, 'MaxIterations',15000000, 'MaxFunctionEvaluations',30000, 'StepTolerance', 0.0000001); [x] = fmincon(objective,tf,A,b,Aeq,beq,lb,ub,nonlincon,options) I am very thankful if somebody can guide me to obtain the values of the variables in the objective function.
