Jordi Castro Constraints matrices with block-angular structures are pervasive in Optimization. Interior-point methods have shown to be competitive for these structured problems by exploiting the linear algebra. One of these approaches solved the normal equations using sparse Cholesky factorizations for the block constraints, and a preconditioned conjugate gradient (PCG) for the linking constraints. The preconditioner is based … Read more
Controlled tabular adjustment (CTA) is an emerging protection technique for tabular data protection. CTA formulates a mixed integer linear programming problem, which is tough for tables of moderate size. Finding a feasible initial solution may even be a challenging task for large instances. On the other hand, end users of tabular data protection techniques give … Read more
Network analysis is of great interest for the study of social, biological and technological networks, with applications, among others, in business, marketing, epidemiology and telecommunications. Researchers are often interested in assessing whether an observed feature in some particular network is expected to be found within families of networks under some hypothesis (named conditional random networks, … Read more
The computational time required by interior-point methods is often dominated by the solution of linear systems of equations. An efficient specialized interior-point algorithm for primal block-angular problems has been used to solve these systems by combining Cholesky factorizations for the block constraints and a conjugate gradient based on a power series preconditioner for the linking … Read more
The feasibility pump (FP) [5,7] has proved to be a successful heuristic for finding feasible solutions of mixed integer linear problems (MILPs). FP was improved in [1] for finding better quality solutions. Briefly, FP alternates between two sequences of points: one of feasible so- lutions for the relaxed problem (but not integer), and another of … Read more
One of the main concerns of national statistical agencies (NSAs) is to publish tabular data. NSAs have to guarantee that no private information from specific respondents can be disclosed from the released tables. The purpose of the statistical disclosure control field is to avoid such a leak of private information. Most protection techniques for tabular … Read more
One of the most efficient interior-point methods for some classes of primal block-angular problems solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient for, respectively, the block and linking constraints. Its efficiency depends on the spectral radius—in [0,1)—of a certain matrix in the definition of the preconditioner. Spectral radius close … Read more
The integrated refinery-planning (IRP), an instrumental problem in the petroleum industry, is made of several subsystems, each of them involving a large number of decisions. Despite the complexity of the overall planning problem, this work presents a mathematical model of the refinery operations char acterized by complete horizontal integration of subsystems from crude oil purchase … Read more
The safe dissemination of statistical tabular data is one of the main concerns of National Statistical Institutes (NSIs). Although each cell of the tables is made up of the aggregated information of several individuals, the statistical confidentiality can be violated. NSIs must guarantee that no individual information can be derived from the released tables. One … Read more
The purpose of the traffic assignment problem is to obtain a traffic flow pattern given a set of origin-destination travel demands and flow dependent link performance functions of a road network. In the general case, the traffic assignment problem can be formulated as a variational inequality, and several algorithms have been devised for its efficient … Read more