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As a maths parser is currently not used in this Wiki, we write math equations as formatted text:

  • Scalars are written as small italic letters, e.g. f
  • Vectors are written as small bold letters, e.g. x.
  • Matrices are written in capital bold letters, e.g. C.


a, a additionals, i.e. additional value(s)
f, f objective function(s)
g, g constraint(s)
x, x design variable(s)


Additionals a are additional values in a solution that are for information only and do not influence the optimization. For example, if an optimization problem returns an objective function that is a sum of several values, these values could be added to the solution as additional values a.
Constraints g are criteria that have to be fulfilled. OpenDino defines a constraint g as
  • fulfilled, if g =< 0
  • violated, if g > 0.

The most simple constraint handling in optimization is to add a penalty to the objective function if the constraint is vialoted, resulting in

f + max(0, g).

design variables
The vector of design variables x may consist of real numbers (continuous variables), integers (discrete variables) or both (mixed variables).
An optimization problem must have at least one objective or one constraint. OpenDino requires that the objective(s) f is/are to be minimized. A maximization of a function k can be converted into minimization by using f = -k.
The term solution is used in optimization. One solution (x,f,g,a) consists of a vector of design variables x, the evaluated objective(s) f(x), constraint(s) g(x), and optionally of additional values a.