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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 ...
An interior point method was discovered by Soviet mathematician I. I. Dikin in 1967. [1] The method was reinvented in the U.S. in the mid-1980s. In 1984, Narendra Karmarkar developed a method for linear programming called Karmarkar's algorithm, [2] which runs in provably polynomial time (() operations on L-bit numbers, where n is the number of variables and constants), and is also very ...
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 affine scaling method is an interior point method, meaning that it forms a trajectory of points strictly inside the feasible region of a linear program (as opposed to the simplex algorithm, which walks the corners of the feasible region). In mathematical optimization, affine scaling is an algorithm for solving linear programming problems.
Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication. They are the de facto standard low-level routines for linear algebra libraries; the ...
MATLAB (an abbreviation of "MATrix LABoratory" [22]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
Dantzig–Wolfe decomposition is an algorithm for solving linear programming problems with special structure. It was originally developed by George Dantzig and Philip Wolfe and initially published in 1960. [1] Many texts on linear programming have sections dedicated to discussing this decomposition algorithm. [2][3][4][5][6][7] Dantzig–Wolfe ...
Frank–Wolfe algorithm. The Frank–Wolfe algorithm is an iterative first-order optimization algorithm for constrained convex optimization. Also known as the conditional gradient method, [1] reduced gradient algorithm and the convex combination algorithm, the method was originally proposed by Marguerite Frank and Philip Wolfe in 1956. [2]