Combinatorial optimization | Exchange algorithms | Combinatorial algorithms | Geometric algorithms | Oriented matroids | Optimization algorithms and methods | Linear programming
Criss-cross algorithm
In 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 inequality constraints and nonlinear objective functions; there are criss-cross algorithms for linear-fractional programming problems, quadratic-programming problems, and linear complementarity problems. Like the simplex algorithm of George B. Dantzig, the criss-cross algorithm is not a polynomial-time algorithm for linear programming. Both algorithms visit all 2D corners of a (perturbed) cube in dimension D, the Klee–Minty cube (after Victor Klee and George J. Minty), in the worst case. However, when it is started at a random corner, the criss-cross algorithm on average visits only D additional corners. Thus, for the three-dimensional cube, the algorithm visits all 8 corners in the worst case and exactly 3 additional corners on average. (Wikipedia).
