Mathematical constraints that define ways of finding the best solution
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A problem with five linear constraints (in blue, including the non-negativity constraints). In the absence of integer constraints the feasible set is the entire region bounded by blue, but with integer constraints it is the set of red dots.A closed feasible region of a linear programming problem with three variables is a convex polyhedron.
In mathematical optimization and computer science, a feasible region,feasible set, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints.[1] This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down.
For example, consider the problem of minimizing the function with respect to the variables and subject to and Here the feasible set is the set of pairs (x, y) in which the value of x is at least 1 and at most 10 and the value of y is at least 5 and at most 12. The feasible set of the problem is separate from the objective function, which states the criterion to be optimized and which in the above example is
In many problems, the feasible set reflects a constraint that one or more variables must be non-negative. In pure integer programming problems, the feasible set is the set of integers (or some subset thereof). In linear programming problems, the feasible set is a convex polytope: a region in multidimensional space whose boundaries are formed by hyperplanes and whose corners are vertices.
Constraint satisfaction is the process of finding a point in the feasible region.
^Beavis, Brian; Dobbs, Ian (1990). Optimisation and Stability Theory for Economic Analysis. New York: Cambridge University Press. p. 32. ISBN 0-521-33605-8.
In mathematical optimization and computer science, a feasibleregion, feasible set, or solution space is the set of all possible points (sets of values...
Look up feasibility in Wiktionary, the free dictionary. Feasibility may refer to: Logical possibility, an achievable thing Feasibleregion, a region that...
possible results of Phase I are either that a basic feasible solution is found or that the feasibleregion is empty. In the latter case the linear program...
subject to linear equality and linear inequality constraints. Its feasibleregion is a convex polytope, which is a set defined as the intersection of...
contradictory, and no solution exists; the feasible set is the empty set. unbounded problem is a feasible problem for which the objective function can...
increases to infinity as its argument approaches the boundary of the feasibleregion of an optimization problem. Such functions are used to replace inequality...
of the function. In artificial intelligence search algorithms, the feasibleregion defining the set of all possible solutions In computational geometry...
extreme point of the feasibleregion (e.g. { x ∣ A x ≥ b } {\displaystyle \{x\mid Ax\geq b\}} ) is integral and thus the feasibleregion is an integral polyhedron...
the feasibleregion will be chosen within all the possible and related action. Second, after the preferred option has been chosen, the feasibleregion that...
the tangent line drawn from the point of the risk-free asset to the feasibleregion for risky assets. The tangency point M represents the market portfolio...
this is unknown, estimating the covariance matrix gives the method of feasible generalized least squares (FGLS). However, FGLS provides fewer guarantees...
intelligence, the designer algorithmically or manually refines the feasibleregion of the program's inputs and outputs with each iteration to fulfill...
the variables that satisfies all constraints—that is, a point in the feasibleregion. The techniques used in constraint satisfaction depend on the kind...
x ) = 0 } {\displaystyle \{x\in R:\forall i\in I,f_{i}(x)=0\}} The feasibleregion of a constrained optimization problem is the solution set of the constraints...
objective value of the dual LP at any feasible solution is always a bound on the objective of the primal LP at any feasible solution (upper or lower bound,...
or candidate solutions. The set S is called the search space, or feasibleregion. The rest of this section assumes that minimization of f(x) is desired;...
— a constraint that involves exactly two variables Corner solution Feasibleregion — contains all solutions that satisfy the constraints but may not be...
combinatorial optimization problem and discussed the properties of the feasibleregion called 'a solitaire cone'. In 1999 peg solitaire was completely solved...
finds a feasible point from which to start optimizing, while the second does the actual optimization while staying strictly inside the feasibleregion. Both...
method for convex optimization, which uses the center-of-gravity of the feasibleregion. Physics portal Barycenter Buoyancy Center of percussion Center of...
interior to the feasible domain and the barrier is in place to bias the iterates to remain away from the boundary of the feasibleregion. They are practically...
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