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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 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 ∗.
For the definitions below, we first present the linear program in the so-called equational form: . maximize subject to = and . where: and are vectors of size n (the number of variables);
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 ...
A decision problem is a computational problem where the answer for every instance is either yes or no. An example of a decision problem is primality testing: "Given a positive integer n, determine if n is prime." A decision problem is typically represented as the set of all instances for which the answer is yes. For example, primality testing ...
Many optimization problems can be equivalently formulated in this standard form. For example, the problem of maximizing a concave function can be re-formulated equivalently as the problem of minimizing the convex function . The problem of maximizing a concave function over a convex set is commonly called a convex optimization problem.
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics.Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods.
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.