Jordi Castro

On solving large-scale multistage stochastic problems with a new specialized interior-point approach

  • Jordi Castro
  • Laureano F. Escudero
  • Juan F. Monge
    • Categories Linear, Cone and Semidefinite Programming, Stochastic Programming Tags , , , , ,

    A novel approach based on a specialized interior-point method (IPM) is presented for solving large-scale stochastic multistage continuous optimization problems, which represent the uncertainty in strategic multistage and operational two-stage scenario trees, the latter being rooted at the strategic nodes. This new solution approach considers a split-variable formulation of the strategic and operational structures, for … Read more

    New interior-point approach for one- and two-class linear support vector machines using multiple variable splitting

  • Jordi Castro
    • Categories Data-Mining, Linear, Cone and Semidefinite Programming Tags , , , ,

    Multiple variable splitting is a general technique for decomposing problems by using copies of variables and additional linking constraints that equate their values. The resulting large optimization problem can be solved with a specialized interior-point method that exploits the problem structure and computes the Newton direction with a combination of direct and iterative solvers (i.e., … Read more

    An algorithm for the Microaggregation problem using Column Generation

  • Jordi Castro
  • Claudio Gentile
  • Enric Spagnolo-Arrizabalaga
    • Categories 0-1 Programming, Applications - OR and Management Sciences, Combinatorial Optimization

    The field of Statistical Disclosure Control aims at reducing the risk of re-identification of an individual when disseminating data, and it is one of the main concerns of national statistical agencies. Operations Research (OR) techniques were widely used in the past for the protection of tabular data, but not for microdata (i.e., files of individuals … Read more

    A new interior-point approach for large two-stage stochastic problems

  • Jordi Castro
  • Paula de la Lama
    • Categories Linear, Cone and Semidefinite Programming, Optimization Software Benchmark, Stochastic Programming

    Two-stage stochastic models give rise to very large optimization problems. Several approaches have been devised for efficiently solving them, including interior-point methods (IPMs). However, using IPMs, the linking columns associated to first-stage decisions cause excessive fill-in for the solution of the normal equations. This downside is usually alleviated if variable splitting is applied to first-stage … Read more

    Using interior point solvers for optimizing progressive lens models with spherical coordinates

  • Glòria Casanellas
  • Jordi Castro
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization Tags , , , ,

    Designing progressive lenses is a complex problem that has been previously solved by formulating an optimization model based on Cartesian coordinates. In this work a new progressive lens model using spherical coordinates is presented, and interior point solvers are used to solve this new optimization model. Although this results in a highly nonlinear, nonconvex, continuous … Read more

    A specialized interior-point algorithm for huge minimum convex cost flows in bipartite networks

  • Jordi Castro
  • Stefano Nasini
    • Categories Linear Programming, Network Optimization

    The computation of the Newton direction is the most time consuming step of interior-point methods. This direction was efficiently computed by a combination of Cholesky factorizations and conjugate gradients in a specialized interior-point method for block-angular structured problems. In this work we apply this algorithmic approach to solve very large instances of minimum cost flows … Read more

    Stabilized Benders methods for large-scale combinatorial optimization, with application to data privacy

  • Daniel Baena
  • Jordi Castro
  • Antonio Frangioni
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Cutting Plane Approaches

    The Cell Suppression Problem (CSP) is a challenging Mixed-Integer Linear Problem arising in statistical tabular data protection. Medium sized instances of CSP involve thousands of binary variables and million of continuous variables and constraints. However, CSP has the typical structure that allows application of the renowned Benders’ decomposition method: once the “complicating” binary variables are … Read more

    On geometrical properties of preconditioners in IPMs for classes of block-angular problems

  • Jordi Castro
  • Stefano Nasini
    • Categories Linear Programming Tags , , , ,

    One of the most efficient interior-point methods for some classes of block-angular structured problems solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient for, respectively, the block and linking constraints. In this work we show that the choice of a good preconditioner depends on geometrical properties of the constraints structure. … Read more

    A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method

  • Jordi Castro
  • Stefano Nasini
  • Francisco Saldanha-da-Gama
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches, Linear Programming

    We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either … Read more

    Interior-point solver for convex separable block-angular problems

  • Jordi Castro
    • Categories Convex Optimization, Optimization Software and Modeling Systems

    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