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The optimum is the best or most favorable condition, or the greatest amount or degree possible under specific sets of comparable circumstances. Optimum may also refer to: Optimum (cable brand), a digital cable service; Optimum Releasing, a film and DVD distribution company based in the UK
The term derives from the Latin optimum, meaning "best". To be optimistic, in the typical sense of the word, is to expect the best possible outcome from any given situation. [1] This is usually referred to in psychology as dispositional optimism. It reflects a belief that future conditions will work out for the best. [2]
The constraint is sharp (sometimes optimal) if it cannot be made more restrictive without failing in some cases. For example, for arbitrary non-negative real numbers x, the exponential function e x, where e = 2.7182818..., gives an upper bound on the values of the quadratic function x 2. This is not sharp; the gap between the functions is ...
A thesaurus (pl.: thesauri or thesauruses), sometimes called a synonym dictionary or dictionary of synonyms, is a reference work which arranges words by their meanings (or in simpler terms, a book where one can find different words with similar meanings to other words), [1] [2] sometimes as a hierarchy of broader and narrower terms, sometimes simply as lists of synonyms and antonyms.
For example, if a bounded differentiable function f defined on a closed interval in the real line has a single critical point, which is a local minimum, then it is also a global minimum (use the intermediate value theorem and Rolle's theorem to prove this by contradiction). In two and more dimensions, this argument fails.
The choice among "Pareto optimal" solutions to determine the "favorite solution" is delegated to the decision maker. In other words, defining the problem as multi-objective optimization signals that some information is missing: desirable objectives are given but combinations of them are not rated relative to each other.
So, we require the aspiration level to be at or below the optimum payoff. We can then define the set of satisficing options S as all those options that yield at least A: s ∈ S if and only if A ≤ U(s). Clearly since A ≤ U *, it follows that O ⊆ S. That is, the set of optimum actions is a subset of the set of satisficing options.
Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously.