I have the following objective function:
where is the only positive decision variable. is a function of . is equivalent to given in the equality constraint below. Other variables are positive constants except a = -4.092*(10^-4), b = -2.167. c = 1.408*(10^-5), d = 6.130.
The plot of the objective function is shown below: y is and x is . The objective function value, is z.
We are minimizing a concave objective (continuous surface).
The constraints are given below:
We are minimizing this concave objective so it is a non-convex optimization problem.
What are the algorithms used in gurobi that will search for a solution with an objective of this form with sum of exponentials that are functions of a first order term (and with first order term multiplying one exponential term) then all of that multiplying a first order term?
Are the solutions optimal or sub-optimal? I want to verify gurobi solution by implementing this algorithm.
I have tried 2 pieces of 2nd order polynomials to estimate this surface in Gurobi but even then what algorithms or analytical techniques are used to find the minimum? But what if I want to keep it as accurate as possible by using this exact objective function? What are the analytical techniques then? When I use the exact objective function some solutions take longer to solve than others.
Basically, I want to have a algorithm/technique so that I know what is happening when the solution is found. Then I will be able to compare this theoretical solution and Gurobi output.
Please also refer me to any papers if possible.
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