MATLAB: What function can I use for finding global optima in semi-infinite constraint optimization problem

fseminfGlobal Optimization ToolboxMATLABoptimization

Below is the simplified version of problem I am trying to solve:
Minimize f(x) =l1+l2+l3
Subject to
     20°≤θ1≤160°
     200°≤θ2≤340°
     200°≤θ3≤340°
Where, θ1,θ2,θ3=f(l1,l2,l3,ϕ)
          30°≤ϕ≤150°
I believe this problem falls under semi-infinite constraints problem, how can I find out global optima of it? I read about fseminf function but it only gives local minima. Can it be optimized using GA?

Best Answer

I think a viable strategy would be to discretize ϕ into a finite set of values (say phi=30:150) and apply GA to the discretized problem. Then, take that solution and use it to initialize fseminf as applied to the original semi-infinite problem. Assuming GA does a decent job, you can reasonably expect the initial guess to be good enough so that the local optimization finds a global solution.
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