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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 ...
Choquet's theorem. Choquet's theorem states that for a compact convex subset C of a normed space V, given c in C there exists a probability measure w supported on the set E of extreme points of C such that, for any affine function f on C, f ( c ) = ∫ f ( e ) d w ( e ) . {\displaystyle f (c)=\int f (e)dw (e).} In practice V will be a Banach space.
George Bernard Dantzig (/ ˈdæntsɪɡ /; November 8, 1914 – May 13, 2005) was an American mathematical scientist who made contributions to industrial engineering, operations research, computer science, economics, and statistics. Dantzig is known for his development of the simplex algorithm, [1] an algorithm for solving linear programming ...
Bland's rule. In mathematical optimization, Bland's rule (also known as Bland's algorithm, Bland's anti-cycling rule or Bland's pivot rule) is an algorithmic refinement of the simplex method for linear optimization. With Bland's rule, the simplex algorithm solves feasible linear optimization problems without cycling. [1][2][3]
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 ...
Branch and cut[1] is a method of combinatorial optimization for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some or all the unknowns are restricted to integer values. [2] Branch and cut involves running a branch and bound algorithm and using cutting planes to tighten the linear programming relaxations ...