7 Optimization Tutorials

In this section we demonstrate how to set up basic types of optimization problems. Each short tutorial contains a working example of formulating problems, defining variables and constraints and retrieving solutions.

• The conic interface tutorial

  • Sec. 7.1 (The conic interface tutorial). Linear and conic optimization tutorial using the conic interface. Essential first reading for all users. Shows all the steps of setting up a conic or linear optimization problem, solving it and retrieving the solutions.

  Further basic examples covering a variety of cones:

  • Sec. 7.2 (A gallery of conic examples). Exponential cone, power cone and cone combinations in various settings.

  • Sec. 7.3 (Geometric Programming). A basic tutorial of geometric programming (GP).

• Mixed-integer optimization tutorials (MIO)

  • Sec. 7.4 (Integer Optimization). Shows how to declare integer variables for linear and conic problems and how to set an initial solution.

  • Sec. 7.5 (Disjunctive constraints). Demonstrates how to create a problem with disjunctive constraints (DJC).

• Infeasibility certificates

  • Sec. 7.6 (Retrieving infeasibility certificates). Shows how to retrieve and analyze a primal infeasibility certificate for continuous problems.

• The linear/simplex interface tutorial

  • Sec. 7.7 (The linear/simplex interface tutorial). Tutorial for the linear optimization toolbox, intended mainly to solve linear problems when the simplex algorithm is used, basic solution is required or warm-start is exploited.

For a more in-depth treatment see the following sections:

• Sec. 9 (Case Studies) for more advanced and complicated optimization examples.

• Sec. 9.1 (Portfolio Optimization) for examples related to portfolio optimization.

• Sec. 11 (Problem Formulation and Solutions) for formal mathematical formulations of problems MOSEK can solve, dual problems and infeasibility certificates.