Free module · Calculus & mathematical models
Optimization: Feasibility, Costs & Robust Decisions
Convert forecasts into decisions whose constraints and failure modes can be checked.
feasibility · curvature · duality · robust bounds · transaction costs
The building blocks
An optimizer chooses the best allowed action under a stated objective. First define what is allowed and what “best” measures.
- Write decisions, units and constraints.
- Solve a small example and check the boundaries.
- Change estimates and costs, then compare a simple benchmark.
Lessons in this module
- Exposure constraints before optimization
- Curvature and a bounded quadratic decision
- Derive the fully invested minimum-variance portfolio
- Project a desired allocation onto the long-only simplex
- Trading costs and a no-trade decision
- An uncertainty bound becomes a position penalty
- Read a binding constraint through its shadow price
- Numerical residuals and independent solution checks
Practice and apply
- Reconcile gross exposure — Weights .6, −.4 and .2; common current equity base.
- Solve a bounded quadratic — Monthly μ=.03, penalty a=.1, weight bounds [0,.2].
- Value a small bound relaxation — μ=.03, a=.1; increase the binding upper weight limit .2 to .21.
Work through the practice exercises · Quant development tools