What you will learn
- Grid search
- Constrained optimization
- Regularization
- Sensitivity to initial conditions
Grid search
Grid search evaluates a specified set of candidates. The grid's range and resolution are research choices. A best point at a boundary may indicate an incomplete search or an unstable objective, not a trustworthy universal optimum.
Constrained optimization
Constrained optimization uses mathematical procedures whose assumptions, convergence criteria and scaling matter. A solver reporting success does not prove that inputs are valid or that the economic model is correct.
Regularization
Regularization discourages certain forms of complexity or extreme choices. It can improve stability under some conditions but introduces another parameter and trade-off. Evaluate it rather than treating it as automatic protection from overfitting.
Sensitivity to initial conditions
Initial conditions and local optima can affect nonlinear procedures. Repeat under justified starting conditions and inspect feasibility and objective values. Report sensitivity instead of selecting the most attractive run silently.
Worked example
A nonlinear solver returns different feasible weights from different starting points with similar objective values. Reporting only one weight vector to many decimals conceals uncertainty in the solution.
Try it yourself
Write a results table that reports starting condition, convergence, feasibility, objective and allocation stability.
Show the worked solution
The table should expose all justified runs and their constraints. Similar objectives with very different weights suggest the allocation is weakly identified by the model; a simpler or more stable choice may deserve comparison.
Apply this to your course project
Compare a simple rule with an optimized alternative under perturbation and held-out scenarios.
Keep the calculation inputs, assumptions and decisions with your work. Practical exercises are self-reviewed; the scored knowledge checks assess the questions shown, not an independent certification of practical competence.