.. index:: simple tutorial Overview ========== In this section, you are going to learn how to execute a series of simple optimizations. We're going to work with the Paraboloid component that we defined in the :ref:`basic tutorial `. The equation in the Paraboloid component is a function of two input variables. Our goal is to find the minimum value of this equation over a particular range of interest. First, we will solve this problem with no constraints. Then we will add constraints and solve the problem again. Next we'll take a look at how you can specify analytic derivatives for your components and what effect that has on the optimization. Lastly, We will run a Design of Experiments (DOE) on the problem and plot the results to visually identify the minimum. If we express the problem as a block diagram, we can see how to set it up in OpenMDAO: .. _`OpenMDAO-overview`: .. figure:: Simple1.png :align: center :alt: Diagram shows the Paraboloid component and optimizer with arrows going between them representing the variables and minimization objective. A Simple Optimization Problem The optimizer is the :term:`Driver`. Its job is to manipulate the two design variables (*x* and *y*) to minimize the output of the ``paraboloid`` function (*f*). Both the driver and the component are contained in an :term:`Assembly`, which maintains the connections between the driver and the component and knows how to run the whole analysis.