Estimation of variables from the inequality and equality constraints

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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.
  3 Comments
Torsten
Torsten on 10 Oct 2022
Edited: Torsten on 10 Oct 2022
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.

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Answers (1)

Matt J
Matt J on 7 Oct 2022
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.
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