Branching and Bounding Improvements for Global Optimization Algorithms with Lipschitz Continuity Properties

  • Coralia Cartis
  • Nicholas I. M. Gould
  • Jaroslav M. Fowkes
    • Categories Global Optimization, Nonlinear Optimization Tags ,

    We present improvements to branch and bound techniques for globally optimizing functions with Lipschitz continuity properties by developing novel bounding procedures and parallelisation strategies. The bounding procedures involve nonconvex quadratic or cubic lower bounds on the objective and use estimates of the spectrum of the Hessian or derivative tensor, respectively. As the nonconvex lower bounds … Read more

    Optimization Techniques for the Brazilian Natural Gas Network Planning Problem

  • Sergio V.B. Bruno
  • Welington de Oliveira
  • Leonardo A. M. Moraes
    • Categories Applications - OR and Management Sciences, Supply Chain Management Tags , , , ,

    This work reports on modeling and numerical experience in solving the long-term design and operation planning problem of the Brazilian natural gas network. A stochastic approach to address uncertainties related to the gas demand is considered. Representing uncertainties by finitely many scenarios increases the size of the resulting optimization problem, and therefore the difficulty to … Read more

    Scheduling on uniform nonsimultaneous parallel machines

  • Donald K. Friesen
  • Liliana Grigoriu
    • Categories Approximation Algorithms, Combinatorial Optimization, Scheduling Tags ,

    We consider the problem of scheduling on uniform processors with nonsimultaneous machine available times with the purpose of mini\-mi\-zing the maximum completion time. We give a variant of the Multifit algorithm which generates schedules which end within $1.382$ times the optimal maximum completion times. This results from properties of the Multifit algorithm when used for … Read more

    A Riemannian symmetric rank-one trust-region method

  • Pierre-Antoine Absil
  • Kyle A. Gallivan
  • Wen Huang
    • Categories Nonlinear Optimization

    The well-known symmetric rank-one trust-region method—where the Hessian approximation is generated by the symmetric rank-one update—is generalized to the problem of minimizing a real-valued function over a $d$-dimensional Riemannian manifold. The generalization relies on basic differential-geometric concepts, such as tangent spaces, Riemannian metrics, and the Riemannian gradient, as well as on the more recent notions … Read more

    Forward-Backward and Tseng’s Type Penalty Schemes for Monotone Inclusion Problems

  • Radu Ioan Bot
  • Ernö Robert Csetnek
    • Categories Convex Optimization Tags , , , , , , , ,

    We deal with monotone inclusion problems of the form $0\in Ax+Dx+N_C(x)$ in real Hilbert spaces, where $A$ is a maximally monotone operator, $D$ a cocoercive operator and $C$ the nonempty set of zeros of another cocoercive operator. We propose a forward-backward penalty algorithm for solving this problem which extends the one proposed by H. Attouch, … Read more

    Facially exposed cones are not always nice

  • Vera Roshchina
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , ,

    We address the conjecture proposed by Gabor Pataki that every facially exposed cone is nice. We show that the conjecture is true in the three-dimensional case, however, there exists a four-dimensional counterexample of a cone that is facially exposed but is not nice. CitationCRN, University of BallaratArticleDownload View PDF

    Nonmonotone line search methods with variable sample size

  • Nataša Krejić
  • Nataša Krklec Jerinkić
    • Categories Global Optimization Tags , , ,

    Nonmonotone line search methods for unconstrained minimization with the objective functions in the form of mathematical expectation are considered. The objective function is approximated by the sample average approximation (SAA) with a large sample of fixed size. The nonmonotone line search framework is embedded with a variable sample size strategy such that different sample size … Read more

    New and Improved Conditions for Uniqueness of Sparsest Solutions of Underdetermined Linear Systems

  • Yun-Bin Zhao
    • Categories Combinatorial Optimization, Convex and Nonsmooth Optimization, Global Optimization Tags , , , , ,

    The uniqueness of sparsest solutions of underdetermined linear systems plays a fundamental role in the newly developed compressed sensing theory. Several new algebraic concepts, including the sub-mutual coherence, scaled mutual coherence, coherence rank, and sub-coherence rank, are introduced in this paper in order to develop new and improved sufficient conditions for the uniqueness of sparsest … Read more

    The Complexity of Large-scale Convex Programming under a Linear Optimization Oracle

  • Guanghui Lan
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    This paper considers a general class of iterative optimization algorithms, referred to as linear-optimization-based convex programming (LCP) methods, for solving large-scale convex programming (CP) problems. The LCP methods, covering the classic conditional gradient (CG) method (a.k.a., Frank-Wolfe method) as a special case, can only solve a linear optimization subproblem at each iteration. In this paper, … Read more

    Using diversification, communication and parallelism to solve mixed-integer linear programs

  • Shabbir Ahmed
  • Rodolfo Carvajal
  • Kevin C Furman
  • George L. Nemhauser
  • Vikas Goel
  • Yufen Shao
    • Categories (Mixed) Integer Linear Programming, Optimization Software and Modeling Systems, Parallel Algorithms Tags , , , , ,

    Performance variability of modern mixed-integer programming solvers and possible ways of exploiting this phenomenon present an interesting opportunity in the development of algorithms to solve mixed-integer linear programs (MILPs). We propose a framework using multiple branch-and-bound trees to solve MILPs while allowing them to share information in a parallel execution. We present computational results on … Read more