We suggest here a least-change correction to available finite element (FE) solution. This postprocessing procedure is aimed at recovering the monotonicity and some other important properties that may not be exhibited by the FE solution. It is based on solving a monotonic regression problem with some extra constraints. One of them is a linear equality-type … Read more
In this paper we propose the approach to solving several combinatorial optimization problems using local search and genetic algorithm techniques. Initially this approach was developed in purpose to overcome some difficulties inhibiting the application of above-mentioned techniques to the problems of the Questionnaire Theory. But when the algorithms were developed it became clear that them … Read more
We study the problem of packing equal circles in a square from the mathematical programming point of view. We discuss different formulations, we analyse formulation symmetries, we propose some symmetry breaking constraints and show that not only do they tighten the convex relaxation bound, but they also ease the task of local NLP solution algorithms … Read more
For a given linear matrix function $A_1 – B_1XB^*_1$, where $X$ is a variable Hermitian matrix, this paper derives a group of closed-form formulas for calculating the global maximum and minimum ranks and inertias of the matrix function subject to a pair of consistent matrix equations $B_2XB^*_2 = A_2$ and $B_3XB_3^* = A_3$. As applications, … Read more
Stochastic dominance theory provides tools to compare random entities. When comparing random vectors (say X and Y ), the problem can be viewed as one of multi-criterion decision making under uncertainty. One approach is to compare weighted sums of the components of these random vectors using univariate dominance. In this paper we propose new concepts … Read more
Computational molecular biology has emerged as one of the most exciting interdisciplinary fields. It has currently benefited from concepts and theoretical results obtained by different scientific research communities, including genetics, biochemistry, and computer science. In the past few years it has been shown that a large number of molecular biology problems can be formulated as … Read more
In this paper, we study trilinear optimization problems with nonconvex constraints under some assumptions. We first consider the semidefinite relaxation (SDR) of the original problem. Then motivated by So \cite{So2010}, we reduce the problem to that of determining the $L_2$-diameters of certain convex bodies, which can be approximately solved in deterministic polynomial-time. After the relaxed … Read more
In this paper, we conduct a thorough study on the first and second order properties of the Moreau-Yosida regularization of the vector $k$-norm function, the indicator function of its epigraph, and the indicator function of the vector $k$-norm ball. We start with settling the vector $k$-norm case via applying the existing breakpoint searching algorithms to … Read more
We study a generalized job-shop problem called the body shop scheduling problem (bssp). This problem arises from the industrial application of welding in a car body production line, where possible collisions between industrial robots have to be taken into account. bssp corresponds to a job-shop problem where the operations of a job have to follow … Read more
Recently the author introduced a semidefinite upper bound on the square of the stability number of a graph, the inverse theta number, which is proved here to be multiplicative with respect to the strong graph product, hence to be an upper bound for the square of the Shannon capacity of the graph. We also describe … Read more