A global error bound for quadratic perturbation of linear programs

A global error bound for quadratic perturbation of linear programs

Convergence and Error Bound for Perturbation ofLinear

In various penalty/smoothing approaches to solving a linear program, one regularizes the problem by adding to the linear cost function a separable nonlinear function multiplied by a small positive parameter. Popular choices of this nonlinearfunction include the quadraticfunction, the logarithm function, and the x ln(x)-entropy function. Furthermore, the solutions generated by such approaches ma...

A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed-Integer Conic Quadratic Programs

This paper develops a linear programming based branch-and-bound algorithm for mixed integer conic quadratic programs. The algorithm is based on a higher dimensional or lifted polyhedral relaxation of conic quadratic constraints introduced by Ben-Tal and Nemirovski. The algorithm is different from other linear programming based branch-and-bound algorithms for mixed integer nonlinear programs in ...

A Quadratic Lower Bound for Homogeneous Algebraic Branching Programs

An algebraic branching program (ABP) is a directed acyclic graph, with a start vertex s, and end vertex t and each edge having a weight which is an affine form in F[x1, x2, . . . , xn]. An ABP computes a polynomial in a natural way, as the sum of weights of all paths from s to t, where the weight of a path is the product of the weights of the edges in the path. An ABP is said to be homogeneous ...

Linear Reformulations of Integer Quadratic Programs

Let (QP ) be an integer quadratic program that consists in minimizing a quadratic function subject to linear constraints. In this paper, we present several linearizations of (QP ). Many linearization methods for the quadratic 0-1 programs are known. A natural approach when considering (QP ) is to reformulate it into a quadratic 0-1 program. However, this method, that we denote BBL (Binary Binar...