11 Case Studies

In this section we present some case studies in which the Fusion API for C++ 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