Applications – Science and Engineering

Implementation of Infinite Dimensional Interior Point Method for Solving Multi-criteria Linear-Quadratic Control Problem

  • Leonid Faybusovich
  • Takashi Tsuchiya
  • Thanasak Mouktonglang
    • Categories Control Applications, Infinite Dimensional Optimization, Linear, Cone and Semidefinite Programming Tags , ,

    We describe an implementation of an infinite-dimensional primal-dual algorithm based on the Nesterov-Todd direction. Several applications to both continuous and discrete-time multi-criteria linear-quadratic control problems and linear-quadratic control problem with quadratic constraints are described. Numerical results show a very fast convergence (typically, within 3-4 iterations) to optimal solutions Citation Preprint, May, 2004, University of Notre … Read more

    On the Relationship between Bilevel Decomposition Algorithms and Direct Interior-Point Methods

  • Victor DeMiguel
  • Francisco Javier Nogales
    • Categories Constrained Nonlinear Optimization, Multidisciplinary Design Optimization Tags , , ,

    Engineers have been using \emph{bilevel decomposition algorithms} to solve certain nonconvex large-scale optimization problems arising in engineering design projects. These algorithms transform the large-scale problem into a bilevel program with one upper-level problem (the master problem) and several lower-level problems (the subproblems). Unfortunately, there is analytical and numerical evidence that some of these commonly used … Read more

    A Local Convergence Analysis of Bilevel Decomposition Algorithms

  • Victor DeMiguel
  • Walter Murray
    • Categories Multidisciplinary Design Optimization, Nonlinear Optimization Tags , , ,

    Decomposition algorithms exploit the structure of large-scale optimization problems by breaking them into a set of smaller subproblems and a coordinating master problem. Cutting-plane methods have been extensively used to decompose convex problems. In this paper, however, we focus on certain nonconvex problems arising in engineering. Engineers have been using bilevel decomposition algorithms to tackle … Read more

    Three-dimensional quasi-static frictional contact by using second-order cone linear complementarity problem

  • Y. Kanno
  • J.A.C. Martins
  • A. Pinto da Costa
    • Categories Complementarity and Variational Inequalities, Mechanical Engineering, Second-Order Cone Programming

    A new formulation is presented for the three-dimensional incremental quasi-static problems with unilateral frictional contact. Under the assumptions of small rotations and small strains, a Second-Order Cone Linear omplementarity Problem (SOCLCP) is formulated, which consists of complementarity conditions defined by the bilinear functions and the second-order cone constraints. The equilibrium configurations are obtained by using … Read more

    Semidefinite descriptions of cones defining spectral mask constraints

  • Leonid Faybusovich
    • Categories Applications - Science and Engineering, Semi-definite Programming Tags , ,

    We discuss in detail an additive structure of cones of trigonometric polynomials nonnegative on the union of finite number of pairwise disjoint segments of the unit circle. We derive new descriptions of these cones in terms of semidefinite constraints. We explain the results of M. Krein and A. Nudelman providing a description of dual cones … Read more

    A randomized heuristic for scene recognition by graph matching

  • Isabelle Bloch
  • Celso C. Ribeiro
  • Maria Claudia Boeres
    • Categories Biomedical Applications, Graphs and Matroids, Meta Heuristics Tags , , , ,

    We propose a new strategy for solving the non-bijective graph matching problem in model-based pattern recognition. The search for the best correspondence between a model and an over-segmented image is formulated as a combinatorial optimization problem, defined by the relational attributed graphs representing the model and the image where recognition has to be performed, together … Read more

    Solving nonconvex SDP problems of structural optimization with stability control

  • Michal Kočvara
  • Michael Stingl
    • Categories Constrained Nonlinear Optimization, Mechanical Engineering, Semi-definite Programming Tags , , ,

    The goal of this paper is to formulate and solve structural optimization problems with constraints on the global stability of the structure. The stability constraint is based on the linear buckling phenomenon. We formulate the problem as a nonconvex semidefinite programming problem and introduce an algorithm based on the Augmented Lagrangian method combined with the … Read more

    On the modeling and control of delamination processes

  • Michal Kočvara
  • Jiri V. Outrata
    • Categories Constrained Nonlinear Optimization, Mechanical Engineering Tags , , ,

    This paper is motivated by problem of optimal shape design of laminated elastic bodies. We use a recently introduced model of delamination, based on minimization of potential energy which includes the free (Gibbs-type) energy and (pseudo)potential of dissipative forces, to introduce and analyze a special mathematical program with equilibrium constraints. The equilibrium is governed by … Read more

    Using Particle Swarm Optimization for Mixed Integer Non-linear Programming in Process Synthesis

  • Rongshan Bi
  • Xia Yang
    • Categories Applications - Science and Engineering Tags ,

    Process synthesis problems can be mathematically represented as mixed-integer nonlinear programming (MINLP) models, which are often irregular, large and non-convex and difficult to get the overall optimum by traditional method. In this paper, a new method named particle swarm optimization (PSO) is used to solve MINLP problems. By introduced penalty function and used sigmoid function, … Read more

    The dose-volume constraint satisfaction problem for inverse treatment planning with field segments

  • Yair Censor
  • James M. Galvin
  • Darek Michalski
  • Ying Xiao
    • Categories Biomedical Applications Tags , ,

    The prescribed goals of radiation treatment planning are often expressed in terms of dose-volume constraints. We present a novel formulation of a dose-volume constraint satisfaction search for the discretized radiation therapy model. This approach does not rely on any explicit cost function. The inverse treatment planning uses the aperture based approach with predefined, according to … Read more