Near optimal

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A point LaTeX: x that is within a small value, say LaTeX: e > 0, of optimality in some sense. The following are the common measures of nearness:

  • in value: LaTeX: x feasible and LaTeX: 
f(x) \ge f(x^*) - e.
  • in policy: LaTeX: \textstyle ||x - x^*|| \le e.
  • in resource level: LaTeX: 
x \in \argmax \left \{f(y): y \in X, g(y) \le b, h(x) = c \right \},
where LaTeX: \textstyle ||(b, c)|| \le e.

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