Fundamentals of Optimization

Definition 23

The standard form of optimization is

Definition 24

The feasible set of an optimization problem is

Definition 25

Definition 26

Problem Transformations

Sometimes, optimizations in a particular formulation do not admit themselves to be solved easily. In this case, we can sometimes transform the problem into an easier one from which we can easily recover the solution to our original problem. In many cases, we can introduce additional “slack” variable and constraints to massage the problem into a form which is easier to analyze.

Theorem 7 (Epigraphic Constraints)

Theorem 8 (Monotone Objective Transformation)

Robust Optimization

For a “nominal” problem

Definition 27

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