11 Case Studies

In this section we present some case studies in which the Fusion API for Python is used to solve real-life applications. These examples involve some more advanced modeling skills and possibly some input data. The user is strongly recommended to first read the basic tutorials of Sec. 7 (Optimization Tutorials) before going through these advanced case studies.

  • Portfolio Optimization
    • Keywords: Markowitz model, variance, risk, efficient frontier, transaction cost, market impact cost, cardinality constraints
    • Type: Conic Quadratic, Power Cone, Mixed-Integer, Model parametrization
  • Primal SVM
    • Keywords: machine learning, Support-Vector Machine, hyperplane separation, classifier
    • Type: Conic Quadratic
  • 2D Total Variation
    • Keywords: denoising, total variation
    • Type: Conic Quadratic, Model parametrization
  • Multi Processor Scheduling
    • Keywords: scheduling, job allocation, feasible point heuristic
    • Type: Mixed-Integer, Linear Optimization
  • Logistic regression
    • Keywords: machine learning, logistic regression, classifier, log-sum-exp, softplus, regularization
    • Type: Exponential Cone, Quadratic Cone
  • Inner and outer Löwner-John Ellipsoids
    • Keywords: volume optimization, ellipsoidal approximation, determinant, geometric mean, eigenvalues
    • Type: Power Cone, Semidefinite
  • SUDOKU
    • Keywords: combinatorial puzzle, binary variables, integer modeling
    • Type: Integer Optimization, Linear Optimization
  • Travelling Salesman
    • Keywords: TSP, cycle elimination
    • Type: Mixed-Integer, Linear Optimization
  • Nearest Correlation Matrix Problem
    • Keywords: low-rank matrix approximation, trace, Frobenius norm, correlation matrix
    • Type: Semidefinite
  • Semidefinite relaxation of MIQCQO problems
    • Keywords: integer quadratic problems, semidefinite relaxation, approximation, integer least squares
    • Type: Semidefinite, Mixed-Integer Conic Quadratic