In this short paper, we give an upper bound for the number of different basic feasible solutions generated by the dual simplex method with the most negative pivoting rule for LP. The bound is comparable with the bound given by Kitahara and Mizuno (2010) for the primal simplex method. We apply the result to the … Read more
This paper introduces a novel algorithm for the nonnegative matrix factorization and completion problem, which aims to nd nonnegative matrices X and Y from a subset of entries of a nonnegative matrix M so that XY approximates M. This problem is closely related to the two existing problems: nonnegative matrix factorization and low-rank matrix completion, … Read more
We replace one of the assumptions (nondegeneracy assumption) in [9] to show that the main results in [9] still hold. We also provide a simple example to show that the new assumption is satisfied, while the original assumption is not satisfied, with other assumptions being satisfied. This example shows that the new assumption does not … Read more
It’s shown that a number of variational problems can be cast as finding the maxinf-points (or minsup-points) of bivariate functions, coveniently abbreviated to bifunctions. These variational problems include: linear and nonlinear complementarity problems, fixed points, variational inequalities, inclusions, non-cooperative games, Walras and Nash equilibrium problems. One can then appeal to the theory of lopsided convergence … Read more
Given an undirected graph and a positive integer k, the maximum k-colorable subgraph problem consists of selecting a k-colorable induced subgraph of maximum cardinality. The natural integer programming formulation for this problem exhibits two kinds of symmetry: arbitrarily permuting the color classes and/or applying a non-trivial graph automorphism gives equivalent solutions. It is well known … Read more
This paper is concerned with the improved constraints handling in mixed-integer optimization problems. The novel element is the reduction of the number of binary variables used for expressing the complement of a convex (polytopic) region. As a generalization, the problem of representing the complement of a possibly non-connected union of such convex sets is detailed. … Read more