Applications – Science and Engineering

HIPAD – A Hybrid Interior-Point Alternating Direction algorithm for knowledge-based SVM and feature selection

  • Ioannis G. Akrotirianakis
  • Zhiwei (Tony) Qin
  • Amit Chakraborty
  • Xiaocheng Tang
    • Categories Convex and Nonsmooth Optimization, Data-Mining, Quadratic Programming Tags , , , ,

    We consider classification tasks in the regime of scarce labeled training data in high dimensional feature space, where specific expert knowledge is also available. We propose a new hybrid optimization algorithm that solves the elastic-net support vector machine (SVM) through an alternating direction method of multipliers in the first phase, followed by an interior-point method … Read more

    Semi-definite relaxations for optimal control problems with oscillation and concentration effects

  • Mathieu Claeys
  • Didier Henrion
  • Martin Kružík
    • Categories Control Applications, Semi-definite Programming

    Converging hierarchies of finite-dimensional semi-definite relaxations have been proposed for state-constrained optimal control problems featuring oscillation phenomena, by relaxing controls as Young measures. These semi-definite relaxations were later on extended to optimal control problems depending linearly on the control input and typically featuring concentration phenomena, interpreting the control as a measure of time with a … Read more

    High Detail Stationary Optimization Models for Gas Networks: Validation and Results

  • Martin Schmidt
  • Marc C. Steinbach
  • Bernhard M. Willert
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , ,

    Due to strict regulatory rules in combination with complex nonlinear physics, major gas network operators in Germany and Europe face hard planning problems that call for optimization. In part 1 of this paper we have developed a suitable model hierarchy for that purpose. Here we consider the more practical aspects of modeling. We validate individual … Read more

    A Flexible Iterative Solver for Nonconvex, Equality-Constrained Quadratic Subproblems

  • Alp Dener
  • Jason Hicken
    • Categories Constrained Nonlinear Optimization, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs Tags , , , , ,

    We present an iterative primal-dual solver for nonconvex equality-constrained quadratic optimization subproblems. The solver constructs the primal and dual trial steps from the subspace generated by the generalized Arnoldi procedure used in flexible GMRES (FGMRES). This permits the use of a wide range of preconditioners for the primal-dual system. In contrast with FGMRES, the proposed … Read more

    Gas Network Optimization: A comparison of Piecewise Linear Models

  • Carlos M. Correa-Posada
  • Pedro Sanchez-Martan
    • Categories (Mixed) Integer Linear Programming, Chemical Engineering Tags , , , , ,

    Gas network optimization manages the gas transport by minimizing operating costs and fulfilling contracts between consumers and suppliers. This is an NP- hard problem governed by non-convex and nonlinear gas transport functions that can be modeled by mixed integer linear programming (MILP) techniques. Under these methods, piecewise linear functions describe nonlinearities and bi- nary variables … Read more

    Optimal scheduling for replacing perimeter guarding unmanned aerial vehicles

  • Oleg Burdakov
  • Patrick Doherty
  • Jonas Kvarnström
    • Categories Civil and Environmental Engineering, Global Optimization, Scheduling

    Guarding the perimeter of an area in order to detect potential intruders is an important task in a variety of security-related applications. This task can in many circumstances be performed by a set of camera-equipped unmanned aerial vehicles (UAVs). Such UAVs will occasionally require refueling or recharging, in which case they must temporarily be replaced … Read more

    Majorization-minimization procedures and convergence of SQP methods for semi-algebraic and tame programs

  • Jérôme Bolte
  • Edouard Pauwels
    • Categories Applications - Science and Engineering, Nonlinear Optimization Tags , , , , , , , ,

    In view of solving nonsmooth and nonconvex problems involving complex constraints (like standard NLP problems), we study general maximization-minimization procedures produced by families of strongly convex sub-problems. Using techniques from semi-algebraic geometry and variational analysis –in particular Lojasiewicz inequality– we establish the convergence of sequences generated by this type of schemes to critical points. The … Read more

    The Descriptor Continuous-Time Algebraic Riccati Equation. Numerical Solutions and Some Direct Applications

  • Claudiu Dinicu
    • Categories Applications - Science and Engineering, Robust Optimization Tags , , ,

    We investigate here the numerical solution of a special type of descriptor continuous-time Riccati equation which is involved in solving several key problems in robust control, formulated under very general hypotheses. We also give necessary and sufficient existence conditions together with computable formulas for both stabilizing and antistabilizing solutions in terms of the associated matrix … Read more

    Convergence Analysis of Primal-Dual Based Methods for Total Variation Minimization with Finite Element Approximation

  • Wenyi Tian
  • Xiao-Ming Yuan
    • Categories Applications - Science and Engineering Tags , , , ,

    We consider the total variation minimization model with consistent finite element discretization. It has been shown in the literature that this model can be reformulated as a saddle-point problem and be efficiently solved by the primal-dual method. The convergence for this application of the primal-dual method has also been analyzed. In this paper, we focus … Read more

    The robust stabilization problem for discrete-time descriptor systems

  • Claudiu Dinicu
    • Categories Applications - Science and Engineering, Robust Optimization Tags , ,

    We investigate here the robust stabilization problem for the descriptor discrete time systems and build an optimal solution in the case when both the nominal system and the perturbations are given in terms of left coprime factorizations. Moreover our formulas are given straight from the original data, using solely the stabilizing solutions of two Riccati … Read more