A primal-dual second order cone approximations algorithm for symmetric cone programming

This paper presents the new concept of second-order cone approximations for convex conic programming. Given any open convex cone $K$, a logarithmically homogeneous self-concordant barrier for $K$ and any positive real number $r \le 1$, we associate, with each direction $x \in K$, a second-order cone $\hat K_r(x)$ containing $K$. We show that $K$ is … Read more

Solving Method for a Class of Bilevel Linear Programming based on Genetic Algorithms

The paper studies and designs an genetic algorithm (GA) of the bilevel linear programming problem (BLPP) by constructing the fitness function of the upper-level programming problem based on the definition of the feasible degree. This GA avoids the use of penalty function to deal with the constraints, by changing the randomly generated initial population into … Read more

On counting integral points in a convex rational polytope

Given a convex rational polytope $\Omega(b):=\{x\in\R^n_+\,|\,Ax=b\}$, we consider the function $b\mapsto f(b)$, which counts the nonnegative integral points of $\Omega(b)$. A closed form expression of its $\Z$-transform $z\mapsto \mathcal{F}(z)$ is easily obtained so that $f(b)$ can be computed as the inverse $\Z$-transform of $\mathcal{F}$. We then provide two variants of an inversion algorithm. As a … Read more