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The definition of global minimum point also proceeds similarly. If the domain X is a metric space, then f is said to have a local (or relative) maximum point at the point x ∗, if there exists some ε > 0 such that f(x ∗) ≥ f(x) for all x in X within distance ε of x ∗.
The maximum of a subset of a preordered set is an element of which is greater than or equal to any other element of , and the minimum of is again defined dually. In the particular case of a partially ordered set , while there can be at most one maximum and at most one minimum there may be multiple maximal or minimal elements.
The satisfiability problem, also called the feasibility problem, is just the problem of finding any feasible solution at all without regard to objective value. This can be regarded as the special case of mathematical optimization where the objective value is the same for every solution, and thus any solution is optimal.
The theorem is typically interpreted as providing conditions for a parametric optimization problem to have continuous solutions with regard to the parameter. In this case, Θ {\displaystyle \Theta } is the parameter space, f ( x , θ ) {\displaystyle f(x,\theta )} is the function to be maximized, and C ( θ ) {\displaystyle C(\theta )} gives ...
As an example, both unnormalised and normalised sinc functions above have of {0} because both attain their global maximum value of 1 at x = 0. The unnormalised sinc function (red) has arg min of {−4.49, 4.49}, approximately, because it has 2 global minimum values of approximately −0.217 at x = ±4.49.
In microeconomics, the utility maximization problem is the problem consumers face: "How should I spend my money in order to maximize my utility?" It is a type of optimal decision problem . It consists of choosing how much of each available good or service to consume, taking into account a constraint on total spending (income), the prices of the ...
This is the weak maximum principle for harmonic functions. This does not, by itself, rule out the possibility that the maximum of u is also attained somewhere on M. That is the content of the "strong maximum principle," which requires further analysis. The use of the specific function above was very inessential. All that mattered was to have a ...
In telecommunications, electronics and the electrical power industry, the term demand factor is used to refer to the fractional amount of some quantity being used relative to the maximum amount that could be used by the same system. The demand factor is always less than or equal to one.