Applications – Science and Engineering

Sparsity constrained split feasibility for dose-volume constraints in inverse planning of intensity-modulated photon or proton therapy

  • Mark Brooke
  • Margherita Casiraghi
  • Yair Censor
  • Scott Penfold
  • Reinhard W. Schulte
  • Rafal Zalas
    • Categories Biomedical Applications, Convex Optimization Tags , , , , , ,

    A split feasibility formulation for the inverse problem of intensity-modulated radiation therapy (IMRT) treatment planning with dose-volume constraints (DVCs) included in the planning algorithm is presented. It involves a new type of sparsity constraint that enables the inclusion of a percentage-violation constraint in the model problem and its handling by continuous (as opposed to integer) … Read more

    Faster Estimation of High-Dimensional Vine Copulas with Automatic Differentiation

  • Hongbo Dong
  • Haijun Li
  • Wei Li
    • Categories Statistics

    Vine copula is an important tool in modeling dependence structures of continuous-valued random variables. The maximum likelihood estimation (MLE) for vine copulas has long been considered computationally difficult in higher dimensions, even in 10 or 20 dimensions. Current computational practice, including the implementation in the state-of- the-art R package VineCopula, suffers from the bottleneck of … Read more

    A dual Newton strategy for scenario decomposition in robust multi-stage MPC

  • Moritz Diehl
  • Sebastien Gros
  • Emil Klintberg
  • Dimitris Kouzoupis
    • Categories Control Applications

    This paper considers the solution of tree-structured Quadratic Programs (QPs) as they may arise in multi- stage Model Predictive Control (MPC). In this context, sampling the uncertainty on prescribed decision points gives rise to different scenarios that are linked to each other via the so-called non-anticipativity constraints. Previous work suggests to dualize these constraints and … Read more

    A Parameterized Proximal Point Algorithm for Separable Convex Optimization

  • Jianchao Bai
  • Jicheng Li
  • Hongchao Zhang
    • Categories Convex Optimization, Statistics

    In this paper, we develop a Parameterized Proximal Point Algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent with a worst-case $O(1/t)$ convergence rate, where $t$ is the iteration number. By properly choosing the algorithm parameters, numerical experiments … Read more

    A MIQCP formulation for B-spline constraints

  • Bjarne Grimstad
    • Categories (Mixed) Integer Nonlinear Programming, Basic Sciences Applications Tags , , , ,

    This paper presents a mixed-integer quadratically constrained programming (MIQCP) formulation for B-spline constraints. The formulation can be used to obtain an exact MIQCP reformulation of any spline-constrained optimization problem, provided that the polynomial spline functions are continuous. This reformulation allows practitioners to use a general-purpose MIQCP solver, instead of a special-purpose spline solver, when solving … Read more

    Geometry of 3D Environments and Sum of Squares Polynomials

  • Amir Ali Ahmadi
  • Georgina Hall
  • Ameesh Makadia
  • Vikas Sindhwani
    • Categories Applications - Science and Engineering, Semi-definite Programming Tags , , ,

    Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an obstacle) with convex or nearly-convex basic semialgebraic sets, computation of Euclidean distance between two such sets, separation of two convex … Read more

    Mixed-Integer Nonlinear Programming Formulation of a UAV Path Optimization Problem

  • Hans D Mittelmann
  • Shankarachary Ragi
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications Tags , , , ,

    We present a mixed-integer nonlinear programming (MINLP) formulation of a UAV path optimization problem in an attempt to find the globally optimum solution. As objective functions in UAV path optimization problems typically tend to be non-convex, traditional optimization solvers (typically local solvers) are prone to local optima, which lead to severely sub-optimal controls. For the … Read more

    Reliable single allocation hub location problem under hub breakdowns

  • Christoph Buchheim
  • Uwe Clausen
  • Nicolas Kämmerling
  • Borzou Rostami
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Facility Planning and Design Tags , , ,

    The design of hub-and-spoke transport networks is a strategic planning problem, as the choice of hub locations has to remain unchanged for long time periods. However, strikes, disasters or traffic breakdown can lead to the unavailability of a hub for a short period of time. Therefore it is important to consider such events already in … Read more

    Understanding Deep Neural Networks with Rectified Linear Units

  • Raman Arora
  • Amitabh Basu
  • Poorya Mianjy
  • Anirbit Mukherjee
    • Categories Applications - Science and Engineering, Other Topics, Polyhedra

    In this paper we investigate the family of functions representable by deep neural networks (DNN) with rectified linear units (ReLU). We give the first-ever polynomial time (in the size of data) algorithm to train a ReLU DNN with one hidden layer to {\em global optimality}. This follows from our complete characterization of the ReLU DNN … Read more

    HEURISTIC ALGORITHMS FOR DESIGNING UNIMODULAR CODE SEQUENCES WITH PERFORMANCE GUARANTEES

  • Edwin K.P. Chong
  • Hans D Mittelmann
  • Shankarachary Ragi
    • Categories Applications - Science and Engineering Tags , , , ,

    In this study, we develop heuristic methods to solve unimodular quadratic programming (UQP) approximately, which is known to be NP-hard. UQP-type problems appear naturally in radar waveform design and active sensing applications. In the UQP framework, we optimize a sequence of complex variables with unit modulus by maximizing a quadratic function. To solve the UQP … Read more