Applications – Science and Engineering

Combining segment generation with direct step-and-shoot optimization in intensity-modulated radiation therapy

  • Fredrik Carlsson
    • Categories Biomedical Applications, Constrained Nonlinear Optimization Tags , , ,

    A method for generating a sequence of intensity-modulated radiation therapy step-and-shoot plans with increasing number of segments is presented. The objectives are to generate high-quality plans with few, large and regular segments, and to make the planning process more intuitive. The proposed method combines segment generation with direct step-and-shoot optimization, where leaf positions and segment … Read more

    A Numerical Algorithm for Block-Diagonal Decomposition of Matrix *-Algebras, Part I: Proposed Approach and Application to Semidefinite Programming

  • Yoshihiro Kanno
  • Masakazu Kojima
  • Kazuo Murota
  • Sadayoshi Kojima
    • Categories Applications - Science and Engineering, Semi-definite Programming Tags , , , ,

    Motivated by recent interest in group-symmetry in semidefinite programming, we propose a numerical method for finding a finest simultaneous block-diagonalization of a finite number of matrices, or equivalently the irreducible decomposition of the generated matrix *-algebra. The method is composed of numerical-linear algebraic computations such as eigenvalue computation, and automatically makes full use of the … Read more

    Fast Computation of Optimal Contact Forces

  • Stephen Boyd
  • Ben Wegbreit
    • Categories Convex Optimization, Mechanical Engineering, Second-Order Cone Programming Tags , , ,

    We consider the problem of computing the smallest contact forces, with point-contact friction model, that can hold an object in equilibrium against a known external applied force and torque. It is known that the force optimization problem (FOP) can be formulated as a semidefinite programming problem (SDP), or a second-order cone problem (SOCP), and so … Read more

    A multilevel algorithm for solving the trust-region subproblem

  • Philippe L. Toint
  • Melissa Weber-Mendonca
  • Dimitri Tomanos
    • Categories Infinite Dimensional Optimization, Optimization of Systems modeled by PDEs, Unconstrained Optimization Tags , , ,

    We present a multilevel numerical algorithm for the exact solution of the Euclidean trust-region subproblem. This particular subproblem typically arises when optimizing a nonlinear (possibly non-convex) objective function whose variables are discretized continuous functions, in which case the different levels of discretization provide a natural multilevel context. The trust-region problem is considered at the highest … Read more

    Processor Speed Control with Thermal Constraints

  • David Atienza
  • Stephen Boyd
  • Giovanni De Micheli
  • Rajesh Gupta
  • Srinivasan Murali
  • Almir Mutapcic
    • Categories Control Applications, Optimization of Systems modeled by PDEs Tags , , , , ,

    We consider the problem of adjusting speeds of multiple computer processors sharing the same thermal environment, such as a chip or multi-chip package. We assume that the speed of processor (and associated variables, such as power supply voltage) can be controlled, and we model the dissipated power of a processor as a positive and strictly … Read more

    l_1 Trend Filtering

  • Stephen Boyd
  • Dimitry Gorinevsky
  • Seung-Jean Kim
  • Kwangmoo Koh
    • Categories Convex and Nonsmooth Optimization, Other Topics, Statistics Tags , , , , , , ,

    The problem of estimating underlying trends in time series data arises in a variety of disciplines. In this paper we propose a variation on Hodrick-Prescott (H-P) filtering, a widely used method for trend estimation. The proposed l_1 trend filtering method substitutes a sum of absolute values (i.e., l_1-norm) for the sum of squares used in … Read more

    Classification problems with imprecise data through separating hyperplanes

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

    We consider a supervised classification problem in which the elements to be classified are sets with certain geometrical properties. In particular, this model can be applied to deal with data affected by some kind of noise and in the case of interval-valued data. Two classification rules, a fuzzy one and a crisp one, are defined … Read more

    A Sequential Convex Semidefinite Programming Algorithm for Multiple-Load Free Material Optimization

  • Michal Kočvara
  • Günter Leugering
  • Michael Stingl
    • Categories Mechanical Engineering, Multidisciplinary Design Optimization, Semi-definite Programming Tags , ,

    A new method for the efficient solution of free material optimization problems is introduced. The method extends the sequential convex programming (SCP) concept to a class of optimization problems with matrix variables. The basic idea of the new method is to approximate the original optimization problem by a sequence of subproblems, in which nonlinear functions … Read more

    H2-optimal model reduction of MIMO systems

  • Pierre-Antoine Absil
  • Kyle A. Gallivan
  • Paul Van Dooren
    • Categories Applications - Science and Engineering Tags , , ,

    We consider the problem of approximating a $p\times m$ rational transfer function $H(s)$ of high degree by another $p\times m$ rational transfer function $\hat{H}(s)$ of much smaller degree. We derive the gradients of the $H_2$-norm of the approximation error and show how stationary points can be described via tangential interpolation. Citation Technical report UCL-INMA-2007.034, Department … Read more

    Local convergence for alternating and averaged nonconvex projections

  • Adrian Lewis
  • Jérôme Malick
  • Russell Luke
    • Categories Constrained Nonlinear Optimization, Control Applications, Nonsmooth Optimization Tags , , , , , , , ,

    The idea of a finite collection of closed sets having “strongly regular intersection” at a given point is crucial in variational analysis. We show that this central theoretical tool also has striking algorithmic consequences. Specifically, we consider the case of two sets, one of which we assume to be suitably “regular” (special cases being convex … Read more