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1.
  • Strömberg, Ann-Brith, 1961, et al. (författare)
  • Mixed-Integer Linear Optimization: Primal–Dual Relations and Dual Subgradient and Cutting-Plane Methods
  • 2020
  • Ingår i: Numerical Nonsmooth Optimization: State of the Art Algorithms. - Cham : Springer International Publishing. ; , s. 499-547, s. 499-547
  • Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
    • This chapter presents several solution methodologies for mixed-integer linear optimization, stated as mixed-binary optimization problems, by means of Lagrangian duals, subgradient optimization, cutting-planes, and recovery of primal solutions. It covers Lagrangian duality theory for mixed-binary linear optimization, a problem framework for which ultimate success—in most cases—is hard to accomplish, since strong duality cannot be inferred. First, a simple conditional subgradient optimization method for solving the dual problem is presented. Then, we show how ergodic sequences of Lagrangian subproblem solutions can be computed and used to recover mixed-binary primal solutions. We establish that the ergodic sequences accumulate at solutions to a convexified version of the original mixed-binary optimization problem. We also present a cutting-plane approach to the Lagrangian dual, which amounts to solving the convexified problem by Dantzig–Wolfe decomposition, as well as a two-phase method that benefits from the advantages of both subgradient optimization and Dantzig–Wolfe decomposition. Finally, we describe how the Lagrangian dual approach can be used to find near optimal solutions to mixed-binary optimization problems by utilizing the ergodic sequences in a Lagrangian heuristic, to construct a core problem, as well as to guide the branching in a branch-and-bound method. The chapter is concluded with a section comprising notes, references, historical downturns, and reading tips.
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3.
  • Bergsten, Christer, 1949- (författare)
  • Några aspekter av matematikens formelspråk
  • 2008
  • Ingår i: Matematiska språk. Sju essäer om symbolspråkets roll i matematiken.. - Stockholm : Santérus Förlag. - 9789173590181 ; , s. 127-143
  • Bokkapitel (populärvet., debatt m.m.)abstract
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4.
  • Högberg, Björn, et al. (författare)
  • Programmable self-assembly: : Theoretical aspects and DNA-linked nanoparticles
  • 2008
  • Ingår i: Systems Self-Assembly. - Amsterdam : Elsevier. - 9780444528650 ; , s. 245-258
  • Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
    • We briefly present a method for the parameterization of assembly systems derived from their ability to form unique structures. The concept of bond uniqueness is introduced and we show how it influences the number of unique structures that a programmable, or algorithmic, self-assembly system can create. Further, we argue that programmable self-assembly systems create embedded, additional computation that is reflected in the complexity of the generated structures and show how this complexity is related to the bond uniqueness of the building blocks. A brief introduction to sticky graphs, a mathematical tool for modeling self-assembly systems, is given. From the theoretical discussions it becomes clear that building blocks for programmable self-assembly need to have at least four distinct, geometrically separated bonds. A scheme for the production of building blocks with well-directed bonds for programmable self-assembly using DNA-nanoparticles is presented. The introduced procedure is a completely bottom–up approach and can be used to produce quite advanced PSA building blocks like nanoparticle eight-mers with eight bonds. Initial experiments are presented.
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5.
  • Juter, Kristina, 1971- (författare)
  • Learning analysis: Students’ starting point.
  • 2009. - 1
  • Ingår i: <em>Nordic Research in Mathematics Education </em>. - Rotterdam, the Netherlands : Sense Publishers. ; , s. 127-134
  • Bokkapitel (övrigt vetenskapligt/konstnärligt)
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  • Khrennikov, Andrei, 1958- (författare)
  • Quantum-like representation of macroscopic configurations.
  • 2009
  • Ingår i: Quantum Interaction. - Berlin : Springer. - 9783642008337 ; , s. 44-58
  • Bokkapitel (refereegranskat)abstract
    • The aim of this paper is to use a contextual probabilistic model (in the spirit of Mackey, Gudder, Ballentine) to represent and to generalize some results of quantum logic on macroscopic quantum-like (QL) behaviour. The crucial point is that our model provides the QL-representation of macroscopic configurations in terms of complex probability amplitudes – wave functions of such configurations. Thus, instead of the language of propositions which is common in quantum logic, we use the language of wave functions which common in the conventional presentation of QM.
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  • Kiselman, Christer, 1939- (författare)
  • Inledning
  • 2008
  • Ingår i: Människor och matematik. - Göteborg : Göteborgs universitet, NCM. - 9789185143085 ; , s. 1-6
  • Bokkapitel (populärvet., debatt m.m.)
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