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Advanced · Self-paced2026 Edition

Optimization for Finance

The optimisation toolbox behind every portfolio, hedging, and risk-budget problem in modern finance — convex programming, KKT, duality, quadratic programming, conic and stochastic optimisation. Ten modules taught practically: every theorem is followed by the finance problem it solves and the solver call (cvxpy, scipy, MOSEK) that produces the answer.

10

Modules

~9h 20m

Reading time

Advanced

Level

Self-paced

Format

§

Syllabus

  1. 01

    Optimisation — the problem statement

    Decision variables, objective, constraints. Feasibility, local vs global optima, the convex/non-convex split that decides whether your problem is tractable.

    ~45 minModule 01
    →
  2. 02

    Convex sets and convex functions

    Why convexity matters: every local minimum is global. The operations that preserve convexity. Quick tests you can apply by hand.

    ~55 minModule 02
    →
  3. 03

    Unconstrained methods — gradient and Newton

    Gradient descent, step-size rules, Newton's method, BFGS quasi-Newton. Convergence rates, conditioning, and when each beats the others.

    ~60 minModule 03
    →
  4. 04

    Constrained optimisation — the Lagrangian and duality

    Lagrange multipliers, the dual function, weak and strong duality, Slater's condition. The shadow-price interpretation that every economist already half-knows.

    ~60 minModule 04
    →
  5. 05

    KKT conditions

    Karush-Kuhn-Tucker conditions as the workhorse first-order optimality test. Stationarity, primal/dual feasibility, complementary slackness.

    ~55 minModule 05
    →
  6. 06

    Linear programming

    Simplex and interior-point. LP duality. The transportation, blending, and arbitrage formulations a finance team actually runs.

    ~55 minModule 06
    →
  7. 07

    Quadratic programming and mean-variance

    The QP. Markowitz mean-variance as a QP. Adding constraints — long-only, sector caps, turnover. Why the unconstrained MV problem is closed-form.

    ~60 minModule 07
    →
  8. 08

    Conic optimisation — SOCP and SDP

    Second-order cone programs and semidefinite programs. Robust portfolio optimisation, ellipsoidal uncertainty, covariance-shrinkage cones.

    ~55 minModule 08
    →
  9. 09

    Stochastic and robust optimisation

    Scenario-based stochastic programming, chance constraints, CVaR optimisation (Rockafellar-Uryasev), worst-case robust formulations.

    ~60 minModule 09
    →
  10. 10

    Solvers in practice — cvxpy, scipy, MOSEK

    How to formulate a problem so a solver eats it. Modelling languages, warm-starting, infeasibility diagnosis, the pre-flight checklist before you trust a number.

    ~55 minModule 10
    →

How to use this course

Start with module 01 if the material is new; skip ahead if you have prior exposure. Each module is self-contained but the arc is sequential — the projects in the final module assume the toolkit from modules 1-11. Every module ends with key takeaways and a curated further-reading list with primary sources.