Estimation of variables from the inequality and equality constraints

Dear all,

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:

% tf≥0

% 0≤t≤tf

%-((w1/(2*tf))*(tf-t(i))^2)+(w2/(2*tf))*(t(i))^2+ (q2/tf - tf*w2/6)- (q1/tf - tf*w1/6)≤370

%[(w1/h)*(tf-t)+(w2/h)*(t)]≤140;

%(w2-w1/tf)≤300;

%-((w1*tf)/2)+(q2-q1)/tf+((w1-w2)*tf/6)=0;

%((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 estimate the values of the variables in the objective function.

[Torsten]

What do you mean by

minimize tf,w1,w2

?

One by one, the sum of them,... ?

[Muhammad Saeed]

Thanks for the response.All of the variables at the same time.Because w1 is also dependent on tf.So all the varaibales should be considered at the same time while performing the minimization.

[Torsten]

So all the varaibales should be considered at the same time while performing the minimization.

Not possible - only if you use gamultiobj to find a pareto optimum.

Answer 1

[Matt J]

Since there are only 3 variables, you can do a discrete sweep of the bounded box described by lb, ub to find points that satisfy the constraints. If you find none, you might have to conclude that there are no solutions to be found.

If you find one, you can use the one with the smallest objective() value as your initial guess to fmincon.

[Muhammad Saeed]

Dear Matt,

thanks for the response and providing attention to the problem.

Indeed there are four variables because "t" is a continuous variable. Discrete sweep of the bounded box is suitable for all the variables or it can be useful to predict the values for the only one varaible?

[Matt J]

All the variables.