Structural optimization of the Ziegler’s pendulum: singularities and exact optimal solutions

  • Oleg Kirillov
    • Categories Mechanical Engineering, Multidisciplinary Design Optimization, Nonsmooth Optimization Tags , , , , , , , , ,

    Structural optimization of non-conservative systems with respect to stability criteria is a research area with important applications in fluid-structure interactions, friction-induced instabilities, and civil engineering. In contrast to optimization of conservative systems where rigorously proven optimal solutions in buckling problems have been found, for non-conservative optimization problems only numerically optimized designs were reported. The proof … Read more

    First-order Methods of Smooth Convex Optimization with Inexact Oracle

  • Olivier Devolder
  • François Glineur
  • Yurii Nesterov
    • Categories Convex Optimization Tags , , , , ,

    We introduce the notion of inexact first-order oracle and analyze the behaviour of several first-order methods of smooth convex optimization used with such an oracle. This notion of inexact oracle naturally appears in the context of smoothing techniques, Moreau-Yosida regularization, Augmented Lagrangians and many other situations. We derive complexity estimates for primal, dual and fast … Read more

    Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods

  • Hédy Attouch
  • Jérôme Bolte
  • Benar Fux Svaiter
    • Categories Nonlinear Optimization Tags , , , , , , , , , , , ,

    In view of the minimization of a nonsmooth nonconvex function f, we prove an abstract convergence result for descent methods satisfying a sufficient-decrease assumption, and allowing a relative error tolerance. Our result guarantees the convergence of bounded sequences, under the assumption that the function f satisfies the Kurdyka-Lojasiewicz inequality. This assumption allows to cover a … Read more

    Calculating optimal conditions for alloy and process design using thermodynamic and property databases, the FactSage software and the Mesh Adaptive Direct Search algorithm

  • Charles Audet
  • Aïmen E. Gheribi
  • Sébastien Le Digabel
  • Arthur D. Pelton
  • Eve Bélisle
    • Categories Applications - Science and Engineering

    During alloy and process design, it is often desired to identify regions of design or process variables for which certain calculated functions have optimal values under various constraints, for example: compositions of minimum liquidus temperature in an N-component alloy; compositions where the amount of precipitate in a given phase is maximized or minimized during annealing … Read more

    Calculating all local minima on liquidus surfaces using the FactSage software and databases and the Mesh Adaptive Direct Search algorithm

  • Charles Audet
  • Aïmen E. Gheribi
  • Sébastien Le Digabel
  • Arthur D. Pelton
  • Christian Robelin
    • Categories Applications - Science and Engineering

    It is often of interest, for a multicomponent system, to identify the low melting compositions at which local minima of the liquidus surface occur. The experimental determination of these minima can be very time-consuming. An alternative is to employ the CALPHAD approach using evaluated thermodynamic databases containing optimized model parameters giving the thermodynamic properties of … Read more

    Complexity bounds for second-order optimality in unconstrained optimization

  • Coralia Cartis
  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , ,

    This paper examines worst-case evaluation bounds for finding weak minimizers in unconstrained optimization. For the cubic regularization algorithm, Nesterov and Polyak (2006) and Cartis, Gould and Toint (2010) show that at most O(epsilon^{-3}) iterations may have to be performed for finding an iterate which is within epsilon of satisfying second-order optimality conditions. We first show … Read more

    Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion

  • Vitor de Matos
  • Andrew B. Philpott
    • Categories Dynamic Programming, Stochastic Programming Tags , ,

    We consider the incorporation of a time-consistent coherent risk measure into a multi-stage stochastic programming model, so that the model can be solved using a SDDP-type algorithm. We describe the implementation of this algorithm, and study the solutions it gives for an application of hydro-thermal scheduling in the New Zealand electricity system. The performance of … Read more

    The central curve in linear programming

  • Jesús A. De Loera
  • Bernd Sturmfels
  • Cynthia Vinzant
    • Categories Convex Optimization, Linear Programming, Nonlinear Optimization Tags , , , , , , , , , , ,

    The central curve of a linear program is an algebraic curve specified by linear and quadratic constraints arising from complementary slackness. It is the union of the various central paths for minimizing or maximizing the cost function over any region in the associated hyperplane arrangement. We determine the degree, arithmetic genus and defining prime ideal … Read more

    Preconditioning and Globalizing Conjugate Gradients in Dual Space for Quadratically Penalized Nonlinear-Least Squares Problems

  • Serge Gratton
  • Philippe L. Toint
  • Selime Gürol
    • Categories Nonlinear Systems and Least-Squares, Optimization of Simulated Systems, Optimization of Systems modeled by PDEs Tags , , , , ,

    When solving nonlinear least-squares problems, it is often useful to regularize the problem using a quadratic term, a practice which is especially common in applications arising in inverse calculations. A solution method derived from a trust-region Gauss-Newton algorithm is analyzed for such applications, where, contrary to the standard algorithm, the least-squares subproblem solved at each … Read more