# NLP

Nonlinear Optimization, sometimes called Nonlinear Programming (NLP), is concerned with the solution of nonlinear optimization problems of the following form:

min f(x) subject to g(x) <= 0, h(x)=0 for a finite dimensional real vector x.

Algorithms of nonlinear optimization are iterative methods that rely on the evaluation of the functional, the constraints and their derivatives. They tend to find local minimizers of the problem.

# Nonlinear Optimization

**Coordination:**Prof. Dr. Jörg Rambau

**Contact:**Prof. Dr. Jörg Rambau

**Represented in MODUS since**2009/01

**Members with experience in this area:**

**The method "Nonlinear Optimization":**

## What is this?

Nonlinear Optimization, sometimes called Nonlinear Programming (NLP), is concerned with the solution of nonlinear optimization problems of the following form:

min f(x) subject to g(x) <= 0, h(x)=0 for a finite dimensional real vector x.

Algorithms of nonlinear optimization are iterative methods that rely on the evaluation of the functional, the constraints and their derivatives. They tend to find local minimizers of the problem.

## What is it good for?

The formulation of a nonlinear optimization problem is very general and thus the range of applications of nonlinear optimization is very broad. Only in the case where many local minimizers are expected it is necessary to combine nonlinear optimization techniques with combinatorial optimization.

## Where have we applied it?

The members of MODUS have applied this method for the following challenges:

- Optimal combined therapy of cancer models
- Optimal load changes for molten carbonate fuel cells
- Trajectory optimization of hang-gliders
- Trajectory optimization of a hypersonic plane s.t. heat constraints modelled by a pde
- Energy minimal solutions of nonlinear elasticity
- Optimization of hyperthermia cancer treatment