Robust optimization is a distinct approach to optimizations problems that allows for the incorporation of
uncertainty. The usefulness of robust optimization lies in the ability to solve for every realization of the uncertain
parameters. As a result, the problem can be solved for the worst-case scenarios of the entire set...
Traditionally, robust optimization has solved problems based on static decisions which are predetermined by the
decision makers. Once the decisions were made, the problem was solved and whenever a new uncertainty was
realized, the uncertainty was incorporated to the original problem and the entire problem was solved again to
account...
Robust optimization is a subset of optimization theory that deals with a certain measure of robustness vs uncertainty. This balance of robustness
and uncertainty is represented as variability in the parameters of the problem at hand and or its solution [1]. In robust optimization, the modeler
aims to find decisions...
Fuzzy programming is one of many optimization models that deal with optimization under uncertainty. This model can be applied when situations are not clearly
defined and thus have uncertainty, or an exact value is not critical to the problem. For example, categorizing people into young, middle aged and old is...
The chance-constrained method is one of the major approaches to solving optimization problems under various
uncertainties. It is a formulation of an optimization problem that ensures that the probability of meeting a certain
constraint is above a certain level. In other words, it restricts the feasible region so that the...
Non-differentiable optimization is a category of optimization that deals with objective that for a variety of reasons
is non differentiable and thus non-convex. The functions in this class of optimization are generally non-smooth.
These functions although continuous often contain sharp points or corners that do not allow for the solution...
Geometric programming was introduced in 1967 by Duffin, Peterson and Zener. It is very useful in the applications
of a variety of optimization problems, and falls under the general class of signomial problems[1]. It can be used to
solve large scale, practical problems by quantifying them into a mathematical optimization...
In this work, we will focus on the “at the same time” or direct transcription approach which allow a simultaneous
method for the dynamic optimization problem. In particular, we formulate the dynamic optimization model with
orthogonal collocation methods. These methods can also be regarded as a special class of implicit...