Global Optimization Applications

Convex Quadratic Relaxations for Mixed-Integer Nonlinear Programs in Power Systems

  • Carleton Coffrin
  • Hassan L. Hijazi
  • Pascal Van Hentenryck
    • Categories Basic Sciences Applications, Convex Optimization, Global Optimization Applications Tags , , , , ,

    This paper presents a set of new convex quadratic relaxations for nonlinear and mixed-integer nonlinear programs arising in power systems. The considered models are motivated by hybrid discrete/continuous applications where existing approximations do not provide optimality guarantees. The new relaxations offer computational efficiency along with minimal optimality gaps, providing an interesting alternative to state-of-the-art semi-definite … Read more

    Global Optimization of Nonlinear Network Design

  • Arvind U. Raghunathan
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Applications

    A novel approach for obtaining globally optimal solutions to design of networks with nonlinear resistances and potential driven flows is proposed. The approach is applicable to networks where the potential loss on an edge in the network is governed by a convex and strictly monotonically increasing function of flow rate. We introduce a relaxation of … Read more

    Numerical Optimization of Eigenvalues of Hermitian Matrix Functions

  • Mustafa Kilic
  • E. Alper Yildirim
  • Emre Mengi
    • Categories Global Optimization Applications, Quadratic Programming Tags , , , ,

    The eigenvalues of a Hermitian matrix function that depends on one parameter analytically can be ordered so that each eigenvalue is an analytic function of the parameter. Ordering these analytic eigenvalues from the largest to the smallest yields continuous and piece-wise analytic functions. For multi-variate Hermitian matrix functions that depend on $d$ parameters analytically, the … Read more

    A Fast Algorithm for Constructing Efficient Event-Related fMRI Designs

  • Ming-Hung Kao
  • Hans D Mittelmann
    • Categories Biomedical Applications, Global Optimization Applications, Multi-Criteria Optimization

    We propose a novel, ecient approach for obtaining high-quality experimental designs for event-related functional magnetic resonance imaging (ER-fMRI). Our approach combines a greedy hillclimbing algorithm and a cyclic permutation method. When searching for optimal ER-fMRI designs, the proposed approach focuses only on a promising restricted class of designs with equal frequency of occurrence across stimulus … Read more

    Squeeze-and-Breathe Evolutionary Monte Carlo Optimisation with Local Search Acceleration and its application to parameter fitting

  • Mauricio Barahona
  • Mariano Beguerisse-Díaz
  • Radhika Desikan
  • Baojun Wang
    • Categories Applications - Science and Engineering, Global Optimization Applications, Systems governed by Differential Equations Optimization Tags , , , ,

    Estimating parameters from data is a key stage of the modelling process, particularly in biological systems where many parameters need to be estimated from sparse and noisy data sets. Over the years, a variety of heuristics have been proposed to solve this complex optimisation problem, with good results in some cases yet with limitations in … Read more

    Global optimization of pipe networks by the interval analysis approach: the Belgium network case

  • Joseph Frédéric Bonnans
  • G. Spiers
  • J.-L. Vie
    • Categories Global Optimization Applications, Network Optimization, Transportation Tags , , ,

    We show that global optimization techniques, based on interval analysis and constraint propagation, succeed in solving the classical problem of optimization of the Belgium gas network. CitationPublished as Inria Research report RR-7796, November 2011.ArticleDownload View PDF

    Approximate spectral factorization for design of efficient sub-filter sequences

  • Mats Andersson
  • Oleg Burdakov
  • Hans Knutsson
  • Björn Norell
    • Categories Constrained Nonlinear Optimization, Global Optimization Applications, Nonlinear Systems and Least-Squares

    A well-known approach to the design of computationally efficient filters is to use spectral factorization, i.e. a decomposition of a filter into a sequence of sub-filters. Due to the sparsity of the sub-filters, the typical processing speedup factor is within the range 1-10 in 2D, and for 3D it achieves 10-100. The design of such … Read more

    Constrained Derivative-Free Optimization on Thin Domains

  • José Mario Martínez
  • Francisco N. C. Sobral
    • Categories Constrained Nonlinear Optimization, Global Optimization Applications, Nonlinear Optimization Tags , , , ,

    Many derivative-free methods for constrained problems are not efficient for minimizing functions on “thin” domains. Other algorithms, like those based on Augmented Lagrangians, deal with thin constraints using penalty-like strategies. When the constraints are computationally inexpensive but highly nonlinear, these methods spend many potentially expensive objective function evaluations motivated by the difficulties of improving feasibility. … Read more

    Proximal point method on Finslerian manifolds and the “Effort Accuracy Trade off”

  • J. X. da Cruz Neto
  • Paulo Roberto Oliveira
  • Antoine Soubeyran
  • Pedro A. Soares Jr.
    • Categories Applications - Science and Engineering, Global Optimization Applications, Nonlinear Optimization

    In this paper we consider minimization problems with constraints. We will show that if the set of constraints is a Finslerian manifold of non positive flag curvature, and the objective function is di fferentiable and satisfi es the property Kurdyka-Lojasiewicz, then the proximal point method is naturally extended to solve that class of problems. We will prove … Read more

    On DC. optimization algorithms for solving minmax flow problems

  • Quang Thuy Le
  • Le Dung Muu
    • Categories Global Optimization Applications, Network Optimization

    We formulate minmax flow problems as a DC. optimization problem. We then apply a DC primal-dual algorithm to solve the resulting problem.The obtained computational results show that the proposed algorithm is efficient thanks to particular structures of the minmax flow problems. Citation1. An L. T. H. and Tao P. D., The DC (Difference of convex … Read more