Linear programming Terminology
- optimization
- To determine the best or most effective use of a resource. Typically expressed as minimizing or maximizing some quantity.
- maximization
- To make something as large as possible. In mathematical terms to determine the largest value a function takes.
- minimization
- To make something as small as possible. In mathematical terms to determine the smallest value a function takes.
- objective function
- The function whose value is to be optimized. Also referred to as: loss function and cost function in minimization; utility function and fitness function in maximization.
- constraints
- A restriction on the values a quantity (and thus the variable representing it) may take. The constraints determine the boundary of the feasible set.
- solution space or feasible set
- The set of all physically possible (feasible) solutions to a problem. In two-dimensional problems this can often be visualized as a region of a plane, and so as a region or space.
- vertex
- A point where two line segments meet.
- theorem
- A statement that has been proven to be true. It provides an iron clad guarantee of truth, and, used
appropriately, correctness. The sun may or may not rise tomorrow—despite all the experimental evidence
we have that it does so every day, we will have to wait and see what happens tomorrow—but 1+1 will
still be equal to 2, whether or not the sun rises.
More generally, each field has its test(s) for truth, or at least for what ought to be believed:- Historians prize textual research, they look to recorded facts and their interpretation to determine whether a statement is true.
- Scientists prize experiments, they weigh the empirical evidence supporting (and denying) a claim to determine if it is true.
- Lawyers look to the outcomes of adversarial trials to determine what on a balance of probabilities is true.
- Archaeologists interpret the physical remains of the past to draw conclusions.
Mathematicians accept as true only those statements that can be proven by a rigorous process of deduction to follow from a set of axioms.
- axiom
- An axiom is a statement that is taken to be true. Its truth is assumed and not able to be proven. Mathematicians aim to have as few axioms (unproven statements) as possible. Also referred to as postulates, assumptions, and premises.
- proof
- A mathematical proof is an argument for a statement that shows that it follows logically from some axioms.