# Optimization

MOSAICmodeling enables a number of different advanced features based on the simulation of steady-state or dynamic system. Among these are the simultaneous and sequential optimization. A number of additional features, such as parameter estimation and chance-constrained optimization will be added subsequently.

Optimization inside MOSAICmodeling is currently limited to general Mixed-Integer NonLinear Programming (MINLP) problems:

$\min_{u,y} f(x,u,y)$

s.t. $g(x,u,y) = 0$,

$x^L \leq x \leq x^U$,

$u^L \leq u \leq u^U$,

$y \in \mathcal{Z}^n$,

$y^L \leq y \leq y^U$

Inequality constraints at the moment need to be manually reformulated as equality constraints by the introduction of slack variables $s$:

$h(x,u,y) \geq 0$ $\Rightarrow h(x, u, y) - s = 0$ with $s \geq 0$

### Advanced Optimization Features

Follow the links below for detailed descriptions on how to use each feature.