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Criss-cross Algorithm
In optimization (mathematics), mathematical optimization, the criss-cross algorithm is any of a family of algorithms for linear programming. Variants of the criss-cross algorithm also solve more general problems with linear programming, linear inequality constraints and nonlinear programming, nonlinear optimization (mathematics), objective functions; there are criss-cross algorithms for linear-fractional programming problems, quadratic programming, quadratic-programming problems, and linear complementarity problems. Like the simplex algorithm of George Dantzig, George B. Dantzig, the criss-cross algorithm is not a time complexity, polynomial-time algorithm for linear programming. Both algorithms visit all 2''D'' corners of a (perturbed) unit cube, cube in dimension ''D'', the Klee–Minty cube (after Victor Klee and George J. Minty), in the worst-case complexity, worst case. However, when it is started at a random corner, the criss-cross algorithm Average-case com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unitcube
A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long.. See in particulap. 671. The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units.. Unit hypercube The term ''unit cube'' or unit hypercube is also used for hypercubes, or "cubes" in N-dimensional space, ''n''-dimensional spaces, for values of ''n'' other than 3 and edge length 1. Sometimes the term "unit cube" refers in specific to the set [0, 1]''n'' of all ''n''-tuples of numbers in the interval [0, 1]. The length of the longest diagonal of a unit hypercube of ''n'' dimensions is \sqrt n, the square root of ''n'' and the (Euclidean) length of the vector (1,1,1,....1,1) in ''n''-dimensional space. See also *Doubling the cube *k-cell (mathematics), ''k''-cell *Robbins constant, the average distance between two random points in a unit cube *Tychonoff cube, an infinite-dimensional analogue of the unit cube *Unit square *Unit sphere R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
