# Optimization Software System

An Optimization Software System is a mathematical software system that can implement a mathematical optimization algorithm to solve a mathematical optimization task.

**Context:**- It can range from being a Combinatorial Optimization System to being a Continuous Optimization System.
- It can range from being a Constrained Optimization System to being a Un-Constrained Optimization System.
- It can range from being a Batch Optimization System to being a Real-Time Optimization System.

**Example(s):****Counter-Example(s):****See:**Optimization Task, Linear System, Constraint (Mathematics), MLE System, Function Parameter Estimator.

## References

### 2016

- (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/List_of_optimization_software Retrieved:2016-7-22.
- Given a transformation between input and output values, described by a mathematical function
*f*, optimization deals with generating and selecting a best solution from some set of available alternatives, by systematically choosing input values from within an allowed set, computing the output of the function, and recording the best output values found during the process. Many real-world problems can be modeled in this way. For example, the inputs can be design parameters of a motor, the output can be the power consumption, or the inputs can be business choices and the output can be the obtained profit.An optimization problem, in this case a minimization problem, can be represented in the following way

*Given:*a function*f*:*A*[math]\displaystyle{ \to }[/math]**R**from some set*A*to the real numbers.*Search for:*an element*x*_{0}in*A*such that*f*(*x*_{0}) ≤*f*(*x*) for all*x*in*A*.

- In continuous optimization,
*A*is some subset of the Euclidean space**R**^{n}, often specified by a set of*constraints*, equalities or inequalities that the members of*A*have to satisfy. In combinatorial optimization,*A*is some subset of a discrete space, like binary strings, permutations, or sets of integers.The use of

**optimization software**requires that the function*f*is defined in a suitable programming language and connected at compile or run time to the optimization software. The optimization software will deliver input values in*A*, the software module realizing*f*will deliver the computed value*f*(*x*) and, in some cases, additional information about the function like derivatives.

In this manner, a clear separation of concerns is obtained: different optimization software modules can be easily tested on the same function*f*, or a given optimization software can be used for different functions*f*.

The following tables provide a list of optimization software organized according to license and business model type.

- Given a transformation between input and output values, described by a mathematical function