An optimization package in python

# oppy

## Optimization Package 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 non-linear optimization problems, the package contains built-in iterative methods for solving linear systems.

Advanced methods for optimization are included such as SQP (Square Quadratic Programming), Augmented Lagrangian and different newton-type 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. If you want to install oppy use

pip install git+https://gitlab.inf.uni-konstanz.de/ag-volkwein/oppy


## Available subpackages

### conOpt

Subpackage which provide some methods for constraint optimization. For problems which are subject to equality and inequality constraints like

min f(x)
s.t. e(x) = 0
g(x) <= 0


we can use

• Penalty Method
• Augmented Lagrangian Method
• SQP with a BFGS update strategy (at the moment only equality constraint)

and for box constraint problems like

min f(x)
s. t. x_a <= x <= x_b


we can use

• The L-BFGS-B Method
• Projected Newton-Krylov Method (if you can provide the action of the second derivative)

### itMet

Iterative methods for solving linear systems like

Ax = b.


Here we can use either stationary methods like

• Jacobi
• GauÃŸ-Seidel
• SOR

or we use krylov methods like

• steepest descent
• CG
• GMRES

For future release we are planing to add preconditioning in the krylov methods. There of course you will be able to use the stationary methods as precondition method.

### linOpt

Linear optimization methods. With the methods in this subpackage we can either solve linear least-squares problem like

min ||Ax - b||_2


or we solve linear programming

max  c^T x
s. t. Ax <= b
x <= 0


with or without integer constraints. For that kind of problems we have the following methods:

• linear least square
• simplex
• branch and bound

### multOpt

Scalarization methods for solving (possibly box-constrained) multiobjective optimization problems of the form

min (f_1(x), ..., f_k(x)),
s.t. x_a <= x <= 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

• Weighted-Sum Method (WSM)
• Euclidean Reference Point Method (ERPM)
• Pascoletti-Serafini 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 f(x)


Right now we can solve this kind of problems with line search based first- and second-order methods.

• Line Search Methods
• Armijo
• Wolfe-Powell
• Optimization Methods
• Newton Method
• Nonlinear CG (with different strategies like Fletcher-Reves)
• Quasi-Newton Methods (with different strategies like BFGS, Broyden, DFP, ...)

### visualization

Some methods for visualization.

## Project details

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