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Mathematics Department

Colloquium Series

Spring 2017

All talks are from 3:45-4:45 p.m. in the Colloquium room, unless otherwise specified.

Tea and cookies will be served in the Lecture room starting at 3:30 p.m.

  • Apr
    12
  • TBA
    Prof. Roberto Camassa
    University of North Carolina
    Time: 03:45 PM
  • Mar
    01
  • Lagrangian Relaxation of the Defender-Attacker-Defender Constrained Shortest Path Problem
    CDR Gary Lazzaro
    USNA
    Time: 03:45 PM

    View Abstract

    Tri-level Defender Attacker-Defender (DAD) optimization models have never been applied to the constrained shortest path problem before. The particular challenge associated the DAD constrained shortest path problem is that an additional side constraint breaks the network structure of a shortest path problem into a more complicated tri-level integer program. We create new solution procedures for the DAD constrained shortest path problem. We merge the attacker model with Lagrangian relaxation of the operator model into a single formulation that can obtain fast heuristic solutions. We combine our heuristic algorithm with traditional methods to obtain provably optimal or near-optimal solutions. We test our algorithms on medium and large networks, and our results show that our innovations can significantly outperform traditional nested decomposition.
  • Feb
    08
  • Tri-Level Optimization Algorithms for Solving Defender-Attacker-Defender Network Models
    CDR Gary Lazzaro
    USNA
    Time: 03:45 PM

    View Abstract

    The optimal defense and operation of networks against worst-case attack is an important problem for military analysts. We review development of existing solutions for the Defender-Attacker-Defender (DAD) tri-level optimization model and investigate new applications and solution procedures. We develop an implicit enumeration algorithm that incorporates addition of new defenses as an alternative solution method for the DAD model. Our testing demonstrates that implicit enumeration can efficiently generate all equivalent optimal or near-optimal solutions for DAD problems. When budgets for network defense or attack are uncertain, decision makers usually prioritize defenses in nested lists. We quantify the costs of various strategies for nesting of defenses. We design a parametric programming formulation of the DAD model to find nested defenses that have the smallest cost difference from optimal non-nested solutions.
  • Jan
    31
  • How the Rules of Engagement Affect the Emergence of Consensus
    Prof. Eitan Tadmor
    University of Maryland
    Location: Rickover 102
    Time: 07:00 PM

    View Abstract

    Opinion dynamics in human crowds and flocking of birds are two prototypical examples for systems which are driven by the "social engagement" of members in such crowds. The "social engagements" are formulated by certain rules which quantify how each member is interacts with its neighbors. These local interactions may lead, over time, to global patterns of the whole crowd, such as the emergence of consensus of opinions, flocking of birds etc. We explore the question how specific rules of interaction lead to the emergence of consensus/flocking.
  • Jan
    19
  • On a class of multiscale problems arising in oceanic and atmospheric processes
    Time: 03:45 PM

    View Abstract

    For the last few years I have been working on a set of problems ​in ocean and atmosphere dynamics. They including modeling sea-ice's melting and reemergence, laser beam propagation in a turbulent medium, and formation of tornadoes. These problems have the common feature of possessing temporal and spatial scales that range over a dozen orders of magnitude. Their mathematical models almost always end up being turbulent dynamical systems with large positive Lyapunov exponents, and very large dimensional phase spaces. While these problems are exceeding difficult, we are fortunate in the last two decades to have access to field data to inform our models. Machine learning in combination with solving PDEs numerically, and incorporating data assimilation are the techniques explored to get a handle on the level of complexity these problems present. In this talk I will introduce three problems and discuss various approaches we have taken to analyze them.
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