[Ipopt] Improving Solution By Adding Constraint On Objective Function

[Frank Kampas]

I’ve observed that constraining the objective function to be <= a number can cause Ipopt to look further and find a better solution, in some instances.
The following results were done in my Mathematica interface to Ipopt.

Constraining the objective function to be <= –2 improved the solution from – 0.71 to – 2.39.  Of course, in some cases,
I get an infeasible problem.

expr = Exp[Sin[50*x]] + Sin[60*Exp[y]] + Sin[70*Sin[x]] + Sin[Sin[80*y]] - Sin[10*(x+y)] + (x^2+y^2)/4;

callIpOpt[ expr, {} , {{x, –1 ,0, 1}, {y, -1, 0, 1}}] [[{1,2,-1}]]
{-0.713075, {x –> -0.0223022, y –> -0.00472762}, Solve_Succeeded}

callIpOpt[ obj, {obj == expr, obj <=  -2}, {{obj, -5, –2 ,0}, {x, -1, 0, 1}, {y, -1, 0, 1 }}] [[{1,2,-1}]]
{-2.38833, {obj- > -2.38833, x –> 0.344918, y –> -0.887746}, Solve_Succeeded}

Are there any option settings which could enhance this property?

Thanks

Frank Kampas

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