Decision variable
The unknown the optimizer chooses. In portfolio allocation, this is often w, the vector of portfolio weights.
Reference 0001
Optimization Formulation Glossary
A compact map of the terms used to turn a portfolio problem into something a solver can handle.
Problem data
Inputs treated as known while solving: expected returns mu, covariance matrix Sigma, current holdings, costs, bounds, and forecasts.
Objective
The scalar quantity optimized. Portfolio objectives commonly trade expected return against risk and cost.
Constraint
A rule the solution must satisfy, such as full investment, long-only weights, leverage limits, turnover limits, or sector caps.
Feasible set
All portfolios satisfying the constraints. If this set is empty, the optimizer has no legal answer.
Convex problem
A problem where local optima are global optima under the relevant convexity conditions. Convexity is why many portfolio formulations are reliable to solve.
Quadratic program
An optimization problem with a quadratic objective and affine constraints. Long-only mean-variance optimization is a standard example.
Multiperiod optimization
A formulation that chooses a sequence of future trades or holdings, usually executing the first trade and replanning later as forecasts update.
Canonical single-period portfolio form
choose weights w
maximize mu' w - gamma * w' Sigma w - trading_cost(w)
subject to 1' w = 1
w >= 0
other portfolio constraints
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