Computational complexity of parametric linear programming

Computational complexity of parametric linear programming

where A is a matrix of order m × p and rank m, and A is a real valued parameter. It may be required to solve this problem for all real values of A, or for all values of A in some specified interval of the real line. f(A) is a piecewise linear convex function in A. The simplex algorithm for this parametric linear program partitions the real line into intervals, each interval being the optimality...

Parametric Linear Programming

Parametric linear programming is the study of how optimal properties depend on data parametrizations. The study is nearly as old as the field of linear programming itself, and it is important since it highlights how a problem changes as what is often estimated data varies. We present what is a modern perspective on the classical analysis of the objective value’s response to parametrizations in ...

Complexity of Linear Programming

The complexity of linear programming is discussed in the "integer" and "real number" models of computation. Even though the integer model is widely used in theoretical computer science, the real number model is more useful for estimating an algorithm's running time in actual computation. Although the ellipsoid algorithm is a polynomial-time algorithm in the integer model, we prove that it has u...

Linear Programming , Complexity

Computational complexity of stochastic programming problems

Stochastic programming is the subfield of mathematical programming that considers optimization in the presence of uncertainty. During the last four decades a vast amount of literature on the subject has appeared. The researchers in the field have never ceased to emphasize the inherent difficulties in solving stochastic programming problems, without ever giving a theoretical justification of thi...