# 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, factor model, 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

• 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: Geometric Mean 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