Applications – Science and Engineering

A parametric active set method for quadratic programs with vanishing constraints

  • Hans Georg Bock
  • Christian Kirches
  • Andreas Potschka
  • Sebastian Sager
    • Categories Combinatorial Optimization, Control Applications, Quadratic Programming Tags , , ,

    Combinatorial and logic constraints arising in a number of challenging optimization applications can be formulated as vanishing constraints. Quadratic programs with vanishing constraints (QPVCs) then arise as subproblems during the numerical solution of such problems using algorithms of the Sequential Quadratic Programming type. QPVCs are nonconvex problems violating standard constraint qualifications. In this paper, we … Read more

    Global Stability Analysis of Fluid Flows using Sum-of-Squares

  • Sergei Chernyshenko
  • Paul J. Goulart
    • Categories Basic Sciences Applications, Optimization of Systems modeled by PDEs, Robust Optimization

    This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed optimization methods based on sum-of-squares decomposition to construct a polynomial Lyapunov function. We then show how these methods can be extended … Read more

    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

    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

    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

    Global Routing in VLSI Design: Algorithms, Theory, and Computational Practice

  • Antoine Deza
  • Tamás Terlaky
  • Anthony Vannelli
  • Chris Dickson
  • Hu Zhang
    • Categories Integer Programming, VLSI layout Tags , ,

    Global routing in VLSI (very large scale integration) design is one of the most challenging discrete optimization problems in computational theory and practice. In this paper, we present a polynomial time algorithm for the global routing problem based on integer programming formulation with a theoretical approximation bound. The algorithm ensures that all routing demands are … Read more

    The Convex Geometry of Linear Inverse Problems

  • Venkat Chandrasekaran
  • Benjamin Recht
  • Pablo A. Parrilo
  • Alan S. Willsky
    • Categories Applications - Science and Engineering, Convex Optimization, Semi-definite Programming

    In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However in many practical situations of interest, models are constrained structurally so that they only have a few degrees … Read more

    On Computation of Performance Bounds of Optimal Index Assignment

  • Hans D Mittelmann
  • Xiaolin Wu
  • J. Wang
  • X. Wang
    • Categories Applications - Science and Engineering, Combinatorial Optimization, Semi-definite Programming Tags , , , , ,

    Channel-optimized index assignment of source codewords is arguably the simplest way of improving transmission error resilience, while keeping the source and/or channel codes intact. But optimal design of index assignment is an in- stance of quadratic assignment problem (QAP), one of the hardest optimization problems in the NP-complete class. In this paper we make a … Read more