Applications – Science and Engineering

Remark on multi-target,robust linear-quadratic control problem on semi-infinite interval

  • Leonid Faybusovich
  • Thanasak Mouktonglang
    • Categories Control Applications, Infinite Dimensional Optimization Tags ,

    We consider multi-target,robust linear-quadratic control problem on semi-infinite interval. Using functional-analytic approach developed in [2], we reduce this problem to a convex optimization problem on the simplex. Explicit procedure for the reduced optimization problem is described. Citation Preprint, University of Notre Dame, August,2015 Article Download View Remark on multi-target,robust linear-quadratic control problem on semi-infinite interval

    On Theoretical and Numerical Aspects of the Shape Sensitivity Analysis for the 3D Time-dependent Maxwell’s Equations

  • Stephan Schmidt
  • Maria Schütte
  • Andrea Walther
    • Categories Optimization of Systems modeled by PDEs Tags , , , , ,

    We propose a novel approach using shape derivatives to solve inverse optimization problems governed by Maxwell’s equations, focusing on identifying hidden geometric objects in a predefined domain. The target functional is of tracking type and determines the distance between the solution of a 3D time-dependent Maxwell problem and given measured data in an $L_2$-norm. Minimization … Read more

    Thermal Optimization of the Continuous Casting Process using Distributed Parameter Identification Approach — Controlling the Curvature of Solid-Liquid Interface

  • Rouhollah Tavakoli
    • Categories Applications - Science and Engineering, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs

    Thermal optimization of vertical continuous casting process is considered in the present study. The goal is to find the optimal distribution of temperature and interfacial heat transfer coefficients corresponding to the primary and secondary cooling systems, in addition to the pulling speed, such that the solidification along the main axis of strand approaches to the … Read more

    Diffusion Methods for Classification with Pairwise Relationships

  • P. F. Felzenszwalb
  • Benar Fux Svaiter
    • Categories Biomedical Applications, Global Optimization, Graphs and Matroids Tags ,

    We define two algorithms for propagating information in classification problems with pairwise relationships. The algorithms involve contraction maps and are related to non-linear diffusion and random walks on graphs. The approach is also related to message passing and mean field methods. The algorithms we describe are guaranteed to converge on graphs with arbitrary topology. Moreover … Read more

    Semidefinite approximations of the polynomial abscissa

  • Didier Henrion
  • Jean-Bernard Lasserre
  • Tiên-So'n Pham
  • Roxana Hess
    • Categories Control Applications, Nonsmooth Optimization, Semi-definite Programming Tags , , , ,

    Given a univariate polynomial, its abscissa is the maximum real part of its roots. The abscissa arises naturally when controlling linear differential equations. As a function of the polynomial coefficients, the abscissa is H\”older continuous, and not locally Lipschitz in general, which is a source of numerical difficulties for designing and optimizing control laws. In … Read more

    Optimal design of multiphase composites under elastodynamic loading

  • Rouhollah Tavakoli
    • Categories Applications - Science and Engineering, Civil and Environmental Engineering, Mechanical Engineering

    An algorithm is proposed to optimize the performance of multiphase structures (composites) under elastodynamic loading conditions. The goal is to determine the distribution of material in the structure such that the time-averaged total stored energy of structure is minimized. A penalization strategy is suggested to avoid the checkerboard instability, simultaneously to generate near 0-1 topologies. … Read more

    Unconditionally energy stable time stepping scheme for Cahn-Morral equation: application to multi-component spinodal decomposition and optimal space tiling

  • Rouhollah Tavakoli
    • Categories Applications - Science and Engineering, Basic Sciences Applications, Optimization of Systems modeled by PDEs Tags , , , , , ,

    An unconditionally energy stable time stepping scheme is introduced to solve Cahn-Morral-like equations in the present study. It is constructed based on the combination of David Eyre’s time stepping scheme and Schur complement approach. Although the presented method is general and independent to the choice of homogeneous free energy density function term, logarithmic and polynomial … Read more

    Robust truss optimization using the sequential parametric convex approximation method

  • Alfredo Canelas
  • Miguel Carrasco
  • Julio López
    • Categories Global Optimization, Multidisciplinary Design Optimization, Second-Order Cone Programming Tags , , ,

    We study the design of robust truss structures under mechanical equilibrium, displacements and stress constraints. Our main objective is to minimize the total amount of material, for the purpose of finding the most economic structure. A robust design is found by considering load perturbations. The nature of the constraints makes the mathematical program nonconvex. In … Read more

    Near-Optimal Ambiguity sets for Distributionally Robust Optimization

  • Vishal Gupta
    • Categories Robust Optimization, Statistics Tags , ,

    We propose a novel, Bayesian framework for assessing the relative strengths of data-driven ambiguity sets in distributionally robust optimization (DRO). The key idea is to measure the relative size between a candidate ambiguity set and an \emph{asymptotically optimal} set as the amount of data grows large. This asymptotically optimal set is provably the smallest convex … Read more

    Mathematical programming algorithms for spatial cloaking

  • Alberto Ceselli
  • Maria Luisa Damiani
  • Giovanni Righini
  • Diego Valorsi
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering, Combinatorial Optimization Tags , , ,

    We consider a combinatorial optimization problem for spatial information cloaking. The problem requires to compute one or several disjoint arborescences on a graph from a predetermined root or subset of candidate roots, so that the number of vertices in the arborescences is minimized but a given threshold on the overall weight associated with the vertices … Read more