oppy API
oppy: optimization in python
Documentation is available in the docstrings and online here.
The idea behind oppy was to provide some optimization methods which are used in the group of Prof. Dr. Volkwein quite often. After a while oppy grew up to a whole optimization package.
Besides algorithms for solving constrained, unconstrained and nonlinear optimization problems, the package contains builtin iterative methods for solving linear systems.
Advanced methods for optimization are included such as SQP (Square Quadratic Programming), Augmented Lagrangian and different newtontype methods. Furthermore certain Krylov methods are implemented for solving linear systems in a stable way.
The goal is to provide a straightforward integration of the library to other applications such that other methods benefit from it.
The package is still in develop mode.
Available subpackages
 conOpt

Subpackage which provide methods for constraint optimization. Equality and inequality constraint problems
\[\min_{x \in \mathbb{R}^n} f(x)\]subject to
\begin{eqnarray} e(x) & = 0 \\ g(x) & \leq 0 \end{eqnarray}can be solved by
 Penalty method
 Augmented Lagrangian method
 SQP with a BFGS update strategy (at the moment only equality constraint).
For box constraint problems
\[\min_{x \in \mathbb{R}^n} f(x)\]\[\text{s. t. } x_a \leq x \leq x_b\]the following methods are available
 Projected gradient Method
 The LBFGSB Method
 Projected NewtonKrylov Method (if you can provide the action of the second derivative).
 itMet

Iterative methods for solving linear systems
\[Ax = b.\]Here we can use either stationary methods
 Jacobi
 GaußSeidel
 SOR
or Krylov methods
 Steepest descent
 CG
 GMRES
For future release we are planing to add preconditioning in the Krylov methods. Stationary methods can then be used for precondition methods.
 leastSquares

Subpackage which provide some methods for linear and nonlinear least squares problems, e.g:
\[\text{min} Ax  b_2\]and
\[\text{min} \frac{1}{2}f(x)_2^2\]Right now we can solve this kind of problems with the following methods.

 Linear Least Squares

 linear least squares (solving normal equation)

 Nonlinear Least Squares

 GaussNewton algorithm with several choices.
 Linesearch or trustregion based Levenberg Marquard algorithm with several choices.

 linOpt

This subpackage contains solver for linear optimization problems e.g methods to solve
\[\text{max } c^T x\]\[\text{s. t. } Ax \leq b\]\[x \geq 0\]with or without integer constraints. For that kind of problems we have the following methods:
 Simplex
 Branch and bound
 multOpt

Scalarization methods for solving (possibly boxconstrained) multiobjective optimization problems of the form
\[\min_{x \in \mathbb{R}^n} (f_1(x), \ldots, f_k(x)),\]\[\text{s. t. } x_a \leq x \leq x_b.\]The general idea of scalarization methods is to transform the multiobjective optimization problem into a series of scalar optimization problems. which can then be solved by using methods from unconstrained or constrained optimization (see the subpackages unconOpt or conOpt). Here we can use the following three scalarization methods
 WeightedSum method (WSM)
 Euclidean Reference Point method (ERPM)
 PascolettiSerafini method (PSM)
 options
 This subpackage contains the options class for all methods use in oppy.
 results
 This subpackage contains the class for the returns which oppy use.
 tests
 Unittests of oppy.
 unconOpt

Subpackage which provide some methods for unconstrained optimization, e.g:
\[\min_{x \in \mathbb{R}^n} f(x)\]Right now we can solve this kind of problems with line search based first and secondorder methods.

 Line Search methods

 Armijo
 WolfePowell

 Optimization methods

 Gradient method
 Newton method
 Nonlinear CG (with different strategies like FletcherReves)
 QuasiNewton methods (with different strategies like BFGS, Broyden, DFP, …)

 visualization
 Some methods for visualization.
Utility tools
test  Run all oppy unittests
__version__  oppy version string

oppy.
test
(show=False)
Available subpackages
 conOpt
 Subpackage which provides some methods for constraint optimization.
 itMet
 Iterative methods for solving linear systems.
 leastSquares
 Least Squares optimization methods.
 linOpt
 Linear optimization methods.
 multiOpt
 Multiobjective optimization methods.
 options
 Module contains the options class for all methods use in oppy.
 results
 This module contains the class for the returns which oppy use.
 tests
 Unittests of oppy.
 unconOpt
 Subpackage which provides some methods for unconstrained optimization.
 visualization
 Some methods for visualization.