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Linear programming is a special case of mathematical programming (also known as mathematical optimization ). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, which is a set defined as the ...
Basic feasible solution. In the theory of linear programming, a basic feasible solution ( BFS) is a solution with a minimal set of non-zero variables. Geometrically, each BFS corresponds to a vertex of the polyhedron of feasible solutions. If there exists an optimal solution, then there exists an optimal BFS.
In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions. For a polyhedron and a vector , is a basic solution if: All the equality constraints defining. P {\displaystyle P} are active at.
Simplex algorithm. In mathematical optimization, Dantzig 's simplex algorithm (or simplex method) is a popular algorithm for linear programming. [ 1] The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. [ 2] Simplices are not actually used in the method, but one interpretation of it is that it ...
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. [1] [2] It is generally divided into two subfields: discrete optimization and continuous optimization.
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear .
BASIC ( Beginners' All-purpose Symbolic Instruction Code) [ 1] is a family of general-purpose, high-level programming languages designed for ease of use. The original version was created by John G. Kemeny and Thomas E. Kurtz at Dartmouth College in 1963. They wanted to enable students in non-scientific fields to use computers.
If sub-problems can be nested recursively inside larger problems, so that dynamic programming methods are applicable, then there is a relation between the value of the larger problem and the values of the sub-problems. [1] In the optimization literature this relationship is called the Bellman equation.