We consider a primal interior point algorithm for LP. The method uses a search direction obtained by minimizing the original objective over a linearly transformed section of the circular cone circumscribed around the nonnegative orthant. If the latter problem has a finite solution, it provides a lower bound for the optimal objective and a target point specifying a descent direction. Otherwise, ...

We consider the traffic grooming problem, a fundamental network design problem in optical networks. We first review a typical ILP formulation considered in the literature, and we identify two challenges related to this formulation in terms of scalability and wavelengths fragmentation. We then propose a new solution approach that decomposes the traffic grooming problem into two subproblems that ...

Intrauterine undernutrition plays a role in the development of adult hypertension. Most studies are done in male offspring to delineate the mechanisms whereby blood pressure may be raised; however, the vascular mechanisms involved in female offspring are unclear. Female offspring of pregnant Sprague-Dawley rats fed either a control (C; 18%) or a low-protein (LP; 6%) diet during pregnancy were u...

Branch-and-price is a generalization of linear programming (LP) based branch-and-bound specifically designed to handle integer programming (IP) formulations that contain a huge number of variables. The basic idea of branch-and-price is simple. Columns are left out of the LP relaxation because there are too many columns to handle efficiently and most of them will have their associated variable e...

Metric facility location is a well-studied problem for which linear programming methods have been used with great success in deriving approximation algorithms. The capacity-constrained generalizations, such as capacitated facility location (Cfl) and lower-bounded facility location (Lbfl), have proved notorious as far as LP-based approximation is concerned: while there are local-search-based con...

BACKGROUND In the human testis, myofibroblasts are the main cellular components of the lamina propria (LP) of seminiferous tubules. Thickened ('fibrotic') LP and dilated tubules are found in a large number of infertile patients, and myofibroblast dedifferentiation has been described in elderly men. It is not known, however, whether dedifferentiation of myofibroblasts is responsible for disturbe...

One of the running themes in this course is the notion of approximate solutions. Of course, this notion is tossed around a lot in applied work: whenever the exact solution seems hard to achieve, you do your best and call the resulting solution an approximation. In theoretical work, approximation has a more precise meaning whereby you prove that the computed solution is close to the exact or opt...

The last several years have seen an increasing interest in combining the models and methods of optimization with those of constraint programming. Integration of the two was initially impeded by their diierent cultural origins , one having developed largely in the operations research community and the other in the computer science and artiicial intelligence communities. The advantages of merger,...

Given a limited resource (such as bandwidth or memory) we consider the problem of scheduling requests from clients that are given as groups of non-intersecting time intervals. Each request j is associated with a demand (the amount of resource required), dj , a t-interval , which consists of up to t segments, for some t ≥ 1, and a weight, w(j). A schedule is a collection of requests. It is feasi...