# 7 Optimization TutorialsΒΆ

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. 7.1 (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 a Fusion model: initialize it, add variables and constraints and retrieve the solution.

**Conic optimization tutorials (CO)**Basic examples demonstrating various types of conic constraints.

Sec. 7.2 (Conic Quadratic Optimization). A basic example with a quadratic cone (CQO).

Sec. 7.3 (Power Cone Optimization). A basic example with a power cone.

Sec. 7.4 (Conic Exponential Optimization). A basic example with a exponential cone (CEO).

Sec. 7.5 (Geometric Programming). A basic tutorial of geometric programming (GP).

**Semidefinite optimization tutorial (SDO)**Sec. 7.6 (Semidefinite Optimization). Examples showing how to solve semidefinite optimization problems with one or more semidefinite variables.

**Mixed-integer optimization tutorials (MIO)**Sec. 7.7 (Integer Optimization). Shows how to declare integer variables for linear and conic problems and how to set an initial solution.

Sec. 7.8 (Disjunctive constraints). Demonstrates how to create a problem with disjunctive constraints (DJC).

**Reoptimization tutorials**Sec. 7.9 (Model Parametrization and Reoptimization). Shows how to construct a parameterized model.

Sec. 7.10 (Problem Modification and Reoptimization). Other techniques for modifying the model.

**Parallel optimization tutorial**Sec. 7.11 (Parallel optimization). Shows how to optimize models in parallel.

**Infeasibility certificates**Sec. 7.12 (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.