6 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.

• Model setup and linear optimization tutorial (LO)

  • Sec. 6.1 (Linear Optimization). Linear optimization tutorial, recommended first reading for all users. Apart from setting up a linear problem it also demonstrates how to work with an optimizer task: initialize it, add variables and constraints and retrieve the solution.

• Conic optimization tutorials (CO)

  • Sec. 6.2 (From Linear to Conic Optimization). A step by step introduction to programming with affine conic constraints (ACC). Explains all the steps required to input a conic problem. Recommended first reading for users of the conic optimizer.

  Further basic examples demonstrating various types of conic constraints:

  • Sec. 6.3 (Conic Quadratic Optimization). A basic example with a quadratic cone (CQO).

  • Sec. 6.4 (Power Cone Optimization). A basic example with a power cone.

  • Sec. 6.5 (Conic Exponential Optimization). A basic example with a exponential cone (CEO).

  • Sec. 6.6 (Geometric Programming). A basic tutorial of geometric programming (GP).

• Semidefinite optimization tutorial (SDO)

  • Sec. 6.7 (Semidefinite Optimization). Examples showing how to solve semidefinite optimization problems with one or more semidefinite variables.

• Mixed-integer optimization tutorials (MIO)

  • Sec. 6.8 (Integer Optimization). Shows how to declare integer variables for linear and conic problems and how to set an initial solution.

  • Sec. 6.9 (Disjunctive constraints). Demonstrates how to create a problem with disjunctive constraints (DJC).

• Quadratic optimization tutorial (QO, QCQO)

  • Sec. 6.10 (Quadratic Optimization). Examples showing how to solve a quadratic or quadratically constrained problem.

• Reoptimization tutorials

  • Sec. 6.11 (Problem Modification and Reoptimization). Various techniques for modifying and reoptimizing a problem.

• Parallel optimization tutorial

  • Sec. 6.12 (Parallel optimization). Shows how to optimize tasks in parallel.

• Infeasibility certificates

  • Sec. 6.13 (Retrieving infeasibility certificates). Shows how to retrieve and analyze a primal infeasibility certificate for continuous problems.

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

• Sec. 11 (Case Studies) for more advanced and complicated optimization examples.

• Sec. 11.1 (Portfolio Optimization) for examples related to portfolio optimization.

• Sec. 12 (Problem Formulation and Solutions) for formal mathematical formulations of problems MOSEK can solve, dual problems and infeasibility certificates.