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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 ...
The Nelder–Mead method (also downhill simplex method, amoeba method, or polytope method) is a numerical method used to find the minimum or maximum of an objective function in a multidimensional space. It is a direct search method (based on function comparison) and is often applied to nonlinear optimization problems for which derivatives may ...
Revised simplex method. In mathematical optimization, the revised simplex method is a variant of George Dantzig 's simplex method for linear programming. The revised simplex method is mathematically equivalent to the standard simplex method but differs in implementation. Instead of maintaining a tableau which explicitly represents the ...
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).
Pattern search (also known as direct search, derivative-free search, or black-box search) is a family of numerical optimization methods that does not require a gradient. As a result, it can be used on functions that are not continuous or differentiable. One such pattern search method is "convergence" (see below), which is based on the theory of ...
Big M method. In operations research, the Big M method is a method of solving linear programming problems using the simplex algorithm. The Big M method extends the simplex algorithm to problems that contain "greater-than" constraints. It does so by associating the constraints with large negative constants which would not be part of any optimal ...
SIMPLE algorithm. In computational fluid dynamics (CFD), the SIMPLE algorithm is a widely used numerical procedure to solve the Navier–Stokes equations. SIMPLE is an acronym for Semi-Implicit Method for Pressure Linked Equations. The SIMPLE algorithm was developed by Prof. Brian Spalding and his student Suhas Patankar at Imperial College ...
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.