New theorems of the alternative for polynomial constraints (based on the Positivstellensatz from real algebraic geometry) and for linear constraints (generalizing the transposition theorems of Motzkin and Tucker) are proved. Based on these, two Karush-John optimality conditions — holding without any constraint qualification — are proved for single- or multi-objective constrained optimization problems. The first … Read more
We present an analytic center cutting surface algorithm that uses mixed linear and multiple second-order cone cuts. Theoretical issues and applications of this technique are discussed. From the theoretical viewpoint, we derive two complexity results. We show that an approximate analytic center can be recovered after simultaneously adding $p$ second-order cone cuts in $O(p\log(p+1))$ Newton … Read more
We describe an effective method for doing binary-encoded modeling, in the context of 0/1 linear programming, when the number of feasible configurations is not a power of two. Our motivation comes from modeling all-different restrictions. ArticleDownload View PDF
Given a complete graph K = (V , E), with edge weight ce on each edge, we consider the problem of partitioning the vertices of graph K into subcliques that each have at least S vertices, so as to minimize the total weight of the edges that have both endpoints in the same subclique. It … Read more
We develop and apply a novel framework which is designed to extract information in the form of a positive definite kernel matrix from possibly crude, noisy, incomplete, inconsistent dissimilarity information between pairs of objects, obtainable in a variety of contexts. Any positive definite kernel defines a consistent set of distances, and the fitted kernel provides … Read more
We present a compact linearization for a broad class of bilinear 0-1 mixed-integer problems subject to assignment constraints. We apply the linearization to three classes of problems: quadratic assignment, multiprocessor scheduling with communication delays, and graph partitioning, and show that it yields faster solution times. CitationDEI, Politecnico di Milano, Working paper, April 2005.ArticleDownload View PDF
Video on Demand (VoD) is a technology used to provide a number of programs to a number of users on request. In developing a VoD system, a fundamental problem is load balancing, which is further characterized by optimally placing videos to a number of predefined servers and routing the user program requests to available resources. … Read more
In this paper we study the network design arc set with variable upper bounds. This set appears as a common substructure of many network design problems and is a relaxation of several fundamental mixed-integer sets studied earlier independently. In particular, the splittable flow arc set, the unsplittable flow arc set, the single node fixed-charge flow … Read more
Recent developments in integer-programming software systems have tremendously improved our ability to solve large-scale instances. We review the major algorithmic components of state-of-the-art solvers and discuss the options available to users to adjust the behavior of these solvers when default settings do not achieve the desired performance level. Furthermore, we highlight advances towards integrated modeling … Read more
This paper is devoted to basic scheduling problems in which the scheduling cost of a job is not a function of its completion time. Instead, the cost is derived from the integration of a cost function over the time intervals on which the job is processed. This criterion is specially meaningful when job preemption is … Read more