2. Features

2.1. Problems

This package supports two types of optimization problems:

• Linear problems

  \[\begin{split}\text{Maximize}~& c' x \\ \text{Subject to} & \\ A x &= b \\ x_l \leq x & \leq x_u\end{split}\]

• Quadratic problems

  \[\begin{split}\text{Maximize}~& x' Q x + c' x \\ \text{Subject to} & \\ A x & = b \\ x_l \leq x & \leq x_u\end{split}\]

2.2. Objectives

This package supports two types of objectives:

• linear
• quadratic

2.3. Variable types

This package supports five types of variables:

• binary
• integer
• continuous
• semi-integer
• semi-continuous
• partially-integer

2.4. Constraints

This package supports one type of constraint:

• linear

2.5. Solvers

This package supports several solvers:

• Open-source

  • Cbc via CyLP
  • CVXOPT via CVXPY
  • GLPK via optlang
  • quadprog
  • SciPy

• Non-commercial with free academic licenses

  • MINOS via solveME
  • SoPlex via soplex_cython

• Commercial with free academic licenses

  • FICO XPRESS
  • IBM CPLEX
  • Gurobi
  • MOSEL Optimizer

However, as described below, some of the solvers only support some of these features.

2.5.1. Objective types

• Cbc: only supports linear objectives
• GLPK: only supports linear objectives
• quadprog: only supports quadratic objectives

2.5.2. Variable types

• Cbc: only supports binary, integer, and continuous variables
• CVXOPT: only supports continuous variables
• FICO XPRESS: supports all variable types
• GLPK: only supports binary, integer, and continuous variables
• Gurobi: doesn’t support partially integer variables
• IBM CPLEX: doesn’t support partially integer variables
• MINOS: only supports continuous variables
• MOSEK Optimizer: only supports binary, integer, and continuous variables
• quadprog: only supports continuous variables
• Scipy: only supports continuous variables

2.5.3. Constraint types

Cbc, GLPK, and quadprog only support linear constraints. Only SciPy’s COBLYA and SLSQP method support contraints.

2.5.4. Python versions

• CPLEX supports Python 2.7, 3.5, and 3.6

2.5.5. Licensing

• FICO XPRESS: licenses are tied to machines, or a license server must be used
• Gurobi: licenses are tied to machines, or a license server must be used
• IBM CPLEX: No license file or activation is needed
• MINOS: free academic licenses can be obtained from Michael Saunders at Stanford
• MOSEL Optimizer: license files can be used on multiple machines
• SoPlex: free academic licenses can be automatically obtained from the SoPlex website