Formulation
Define variables, objective and constraints so the mathematical problem matches the real decision rather than a convenient surrogate.
Side 214Side Studies / Research
Subject
Optimization
Purpose
Objectives, decision variables and constraints studied through convexity, duality, algorithms and sensitivity.
Structure
05 movesFormal systemV0
Definitions → structures → relations → proof → application
Turn choice into a mathematical problem before solving it.
Optimization is less about finding a maximum than about formulating what is being chosen, what is allowed, and how the solution changes when assumptions move.
Convexity
Recognize structures where local optima are global and powerful guarantees become available.
Optimality conditions
Use gradients, multipliers and subgradients to characterize candidate solutions under constraints.
Duality
Construct alternative formulations that expose bounds, shadow prices and sensitivity to constraints.
Algorithms & sensitivity
Compare iterative methods by convergence and conditioning, then study how solutions change under perturbation.
Keep the boundaries visible.
objective ≠ true value
constraint ≠ fixed physical law
local optimum ≠ global optimum
Questions that organize the Side.
When does a model's objective distort the decision it is supposed to represent?
What structural properties make an optimization problem tractable?
How should sensitivity change confidence in an optimal solution?
What should carry weight here?
Proofs establish optimality conditions; numerical results require convergence diagnostics, conditioning analysis and validation of the formulation itself.