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The term antonym (and the related antonymy) is commonly taken to be synonymous with opposite, but antonym also has other more restricted meanings. Graded (or gradable) antonyms are word pairs whose meanings are opposite and which lie on a continuous spectrum (hot, cold).
Antonyms for effectiveness include: uselessness, ineffectiveness. [13] Simply stated, effective means achieving an effect, and efficient means getting a task or job done it with little waste. To illustrate: suppose, you build 10 houses, very fast and cheap (efficient), but no one buy them.
An optimal decision is a decision that leads to at least as good a known or expected outcome as all other available decision options. It is an important concept in decision theory . In order to compare the different decision outcomes, one commonly assigns a utility value to each of them.
Pareto originally used the word "optimal" for the concept, but this is somewhat of a misnomer: Pareto's concept more closely aligns with an idea of "efficiency", because it does not identify a single "best" (optimal) outcome. Instead, it only identifies a set of outcomes that might be considered optimal, by at least one person. [4]
Inspired by—but distinct from—the Hamiltonian of classical mechanics, the Hamiltonian of optimal control theory was developed by Lev Pontryagin as part of his maximum principle. [2] Pontryagin proved that a necessary condition for solving the optimal control problem is that the control should be chosen so as to optimize the Hamiltonian. [3]
It is an informal antonym for pathological. For example, one might conjecture that a differential operator ought to satisfy a certain boundedness condition "for nice test functions," or one might state that some interesting topological invariant should be computable "for nice spaces X ."
The goal is then to find for some instance x an optimal solution, that is, a feasible solution y with (,) = {(, ′): ′ ()}. For each combinatorial optimization problem, there is a corresponding decision problem that asks whether there is a feasible solution for some particular measure m 0 .
Optimal behavior is defined as an action that maximizes the difference between the costs and benefits of that decision. Three primary variables are used in optimality models of behavior: decisions, currency, and constraints. [2] Decision involves evolutionary considerations of the costs and benefits of their actions.