On the convergence of an inexact Gauss-Newton trust-region method for nonlinear least-squares problems with simple bounds

  • Margherita Porcelli
    • Categories Bound-constrained Optimization, Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , , ,

    We introduce an inexact Gauss-Newton trust-region method for solving bound-constrained nonlinear least-squares problems where, at each iteration, a trust-region subproblem is approximately solved by the Conjugate Gradient method. Provided a suitable control on the accuracy to which we attempt to solve the subproblems, we prove that the method has global and asymptotic fast convergence properties. … Read more

    Globally Solving Nonconvex Quadratic Programming Problems via Completely Positive Programming

  • Samuel Burer
  • Jieqiu Chen
    • Categories Global Optimization, Optimization Software and Modeling Systems, Quadratic Programming Tags , , , ,

    Nonconvex quadratic programming (QP) is an NP-hard problem that optimizes a general quadratic function over linear constraints. This paper introduces a new global optimization algorithm for this problem, which combines two ideas from the literature—finite branching based on the first-order KKT conditions and polyhedral-semidefinite relaxations of completely positive (or copositive) programs. Through a series of … Read more

    A stabilized model and an efficient solution method for the yearly optimal power management

  • Vincent Guigues
    • Categories Applications - OR and Management Sciences

    We propose a stabilized model for the electricity generation management problem on a yearly scale. We also introduce an original and efficient solution method in a particular case. Our model is compared to other management methods and offers the best average cost while preserving a reasonable standard deviation of the cost over a set of … Read more

    A Dual Algorithm For Approximating Pareto Sets in Convex Multi-Criteria Optimization

  • Rasmus Bokrantz
  • Anders Forsgren
    • Categories Biomedical Applications, Multi-Criteria Optimization

    We consider the problem of approximating the Pareto set of convex multi-criteria optimization problems by a discrete set of points and their convex combinations. Finding the scalarization parameters that maximize the improvement in bound on the approximation error when generating a single Pareto optimal solution is a nonconvex optimization problem. This problem is solvable by … Read more

    Robust Production Management

  • Vincent Guigues
    • Categories Robust Optimization

    The problem of production management can often be cast in the form of a linear program with uncertain parameters and risk constraints. Typically, such problems are treated in the framework of multi-stage Stochastic Programming. Recently, a Robust Counterpart (RC) approach has been proposed, in which the decisions are optimized for the worst realizations of problem … Read more

    Sensitivity analysis and calibration of the covariance matrix for stable portfolio selection

  • Vincent Guigues
    • Categories Quadratic Programming

    We recommend an implementation of the Markowitz problem to generate stable portfolios with respect to perturbations of the problem parameters. The stability is obtained proposing novel calibrations of the covariance matrix between the returns that can be cast as convex or quasiconvex optimization problems. A statistical study as well as a sensitivity analysis of the … Read more

    Interior-Point Algorithms for a Generalization of Linear Programming and Weighted Centering

  • Kurt M. Anstreicher
    • Categories Convex Optimization, Linear Programming Tags , , ,

    We consider an extension of ordinary linear programming (LP) that adds weighted logarithmic barrier terms for some variables. The resulting problem generalizes both LP and the problem of finding the weighted analytic center of a polytope. We show that the problem has a dual of the same form and give complexity results for several different … Read more

    Robust mid-term power generation management

  • René Aid
  • Vincent Guigues
  • Papa Momar Ndiaye
  • François Oustry
  • François Romanet
    • Categories Robust Optimization

    We consider robust formulations of the mid-term optimal power management problem. For this type of problems, classical approaches minimize the expected generation cost over a horizon of one year, and model the uncertain future by means of scenario trees. In this setting, extreme scenarios -with low probability in the scenario tree- may fail to be … Read more

    Mean and covariance matrix adaptive estimation for a weakly stationary process. Application in stochastic optimization.

  • Vincent Guigues
    • Categories Stochastic Programming

    We introduce an adaptive algorithm to estimate the uncertain parameter of a stochastic optimization problem. The procedure estimates the one-step-ahead means, variances and covariances of a random process in a distribution-free and multidimensional framework when these means, variances and covariances are slowly varying on a given past interval. The quality of the approximate problem obtained … Read more

    Bound reduction using pairs of linear inequalities

  • Pietro Belotti
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Constrained Nonlinear Optimization Tags , , ,

    We describe a procedure to reduce variable bounds in Mixed Integer Nonlinear Programming (MINLP) as well as Mixed Integer Linear Programming (MILP) problems. The procedure works by combining pairs of inequalities of a linear programming (LP) relaxation of the problem. This bound reduction technique extends the implied bounds procedure used in MINLP and MILP and … Read more