#NONLINEAR REGRESSION EXCEL SOLVER TRIAL#
When the message “Solver has converged to the current solution” appears, it means that the objective function value is changing very slowly for the last few iterations or trial solutions. When Solver has Converged to the Current Solution Mathematically, this message means that the Karush - Kuhn - Tucker (KKT) conditions for local optimality have been satisfied (to within a certain tolerance, related to the Precision setting in the Solver Options dialog). Figuratively, this means that Solver has found a “peak” (if maximizing) or “valley” (if minimizing) – but if the model is non-convex, there may be other taller peaks or deeper valleys far away from the current solution. When the message “Solver found a solution” appears, it means that the GRG method has found a locally optimal solution – there is no other set of values for the decision variables close to the current values that yields a better value for the objective function. Locally Versus Globally Optimal Solutions At times, Solver will stop before finding a locally optimal solution, when it is making very slow progress (the objective function is changing very little from one trial solution to another) or for other reasons. At best, the GRG Solving method alone – like virtually all “classical” nonlinear optimization algorithms – can find a locally optimal solution to a reasonably well-scaled, non-convex model. It is helpful to understand what the GRG Nonlinear Solving method can and cannot do, and what each of the possible Solver Result Messages means for this Solver engine.
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