New Formulations for Optimization Under Stochastic Dominance Constraints

  • James R. Luedtke
    • Categories Stochastic Programming Tags , , , ,

    Stochastic dominance constraints allow a decision-maker to manage risk in an optimization setting by requiring their decision to yield a random outcome which stochastically dominates a reference random outcome. We present new integer and linear programming formulations for optimization under first and second-order stochastic dominance constraints, respectively. These formulations are more compact than existing formulations, … Read more

    Solving the Prize-collecting Rural Postman Problem

  • Julian Araoz
  • Oscar Meza
  • Elena Fernandez
    • Categories Cutting Plane Approaches, Integer Programming Tags ,

    In this work we present an algorithm for solving the Prize-collecting Rural Postman Problem. This problem was recently defined and is a generalization of other arc routing problems like, for instance, the Rural Postman Problem. The main difference is that there are no required edges. Instead, there is a profit function on the edges that … Read more

    Controlling the dose distribution with gEUD-type constraints within the convex IMRT optimization framework

  • Tim Craig
  • Harald Keller
  • Michael Sharpe
  • Tamás Terlaky
  • Yuriy Zinchenko
    • Categories Biomedical Applications, Convex Optimization Tags , , , , , ,

    Radiation therapy is an important modality in treating various cancers. Various treatment planning and delivery technologies have emerged to support Intensity Modulated Radiation Therapy (IMRT), creating significant opportunities to advance this type of treatment. We investigate the possibility of including the dose prescription, specified by the DVH, within the convex optimization framework for inverse IMRT … Read more

    A simple exact separation algorithm for 2-matching inequalities.

  • Julian Araoz
  • Oscar Meza
  • Elena Fernandez
    • Categories Combinatorial Optimization Tags ,

    In this work we present an exact separation algorithm for the so called co-circuit inequalities, otherwise known as parity or 2-matching inequalities. The algorithm is quite simple since it operates on the tree of min-cuts of the support graph of the solution to separate, relative to an ad hoc capacity vector. The order of our … Read more

    On linear infeasibility arising in intensity-modulated radiation therapy inverse planning

  • Adi Ben-Israel
  • Yair Censor
  • James M. Galvin
  • Ying Xiao
    • Categories Applications - Science and Engineering, Approximation Algorithms Tags , , , , ,

    Intensity–modulated radiation therapy (IMRT) gives rise to systems of linear inequalities, representing the effects of radiation on the irradiated body. These systems are often infeasible, in which case one settles for an approximate solution, such as an {a,ß}–relaxation, meaning that no more than a percent of the inequalities are violated by no more than ß … Read more

    Support Vector Regression for imprecise data

  • Emilio Carrizosa
  • José F. Gordillo
  • Frank Plastria
    • Categories Convex Optimization, Data-Mining, Quadratic Programming Tags , , , , ,

    In this work, a regression problem is studied where the elements of the database are sets with certain geometrical properties. In particular, our model can be applied to handle data affected by some kind of noise or uncertainty and interval-valued data, and databases with missing values as well. The proposed formulation is based on the … Read more

    Comparison Between NSGA-II and MOEA/D on a Set of Multiobjective Optimization Problems with Complicated Pareto Sets

  • Hui Li
  • Qingfu Zhang
    • Categories Multi-Criteria Optimization Tags , ,

    Partly due to lack of test problems, the impact of the Pareto set (PS) shapes on the performance of evolutionary algorithms has not yet attracted much attention. This paper introduces a general class of continuous multiobjective optimization test instances with arbitrary prescribed PS shapes, which could be used for studying the ability of MOEAs for … Read more

    Global and adaptive scaling in a separable augmented lagrangian algorithm

  • Arnaud Lenoir
  • Philippe Mahey
    • Categories Convex Optimization Tags ,

    In this paper, we analyze the numerical behaviour of a separable Augmented Lagrangian algorithm with multiple scaling parameters, different parameters associated with each dualized coupling constraint as well as with each subproblem. We show that an optimal superlinear rate of convergence can be theoretically attained in the twice differentiable case and propose an adaptive scaling … Read more

    A partitioning algorithm for the network loading problem

  • Frédéric Babonneau
  • Jean-Philippe Vial
    • Categories Cutting Plane Approaches, Network Optimization Tags , ,

    This paper proposes a Benders-like partitioning algorithm to solve the network loading problem. The effort of computing integer solutions is entirely left to a pure integer programming solver while valid inequalities are generated by solving standard nonlinear multicommodity flow problems. The method is compared to alternative approaches proposed in the literature and appears to be … Read more

    Two theoretical results for sequential semidefinite programming

  • Rodrigo Garcés
  • Walter Gómez
  • Florian Jarre
    • Categories Constrained Nonlinear Optimization, Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems Tags , , , , , ,

    We examine the local convergence of a sequential semidefinite programming approach for solving nonlinear programs with nonlinear semidefiniteness constraints. Known convergence results are extended to slightly weaker second order sufficient conditions and the resulting subproblems are shown to have local convexity properties that imply a weak form of self-concordance of the barrier subproblems. CitationPreprint, Mathematisches … Read more