| 1. |
- Strömberg, Ann-Brith, 1961, et al.
(författare)
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Mixed-Integer Linear Optimization: Primal–Dual Relations and Dual Subgradient and Cutting-Plane Methods
- 2020
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Ingår i: Numerical Nonsmooth Optimization: State of the Art Algorithms. - Cham : Springer International Publishing. ; , s. 499-547, s. 499-547
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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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| 2. |
- Johansson, Maria, et al.
(författare)
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Multidimensional inequalities of Hardy and (limit) Pólya-Knopp types
- 2012
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Ingår i: Analysis for science, engineering and beyond. - Heidelberg : Encyclopedia of Global Archaeology/Springer Verlag. - 9783642202353 - 9783642202360 ; , s. 267-304
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Bokkapitel (refereegranskat)abstract
- In this review paper we complement the classical two-dimensional Hardy-type inequality by E. Sawyer (see MR87f:42052) in various ways. In particular, ideas and results from three recent Ph.D. theses are unified and presented in this frame. Also some complementary new results are proved and some open questions are raised.
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| 3. |
- Juter, Kristina, 1971-
(författare)
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Students’ perceptions of limits
- 2010
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Ingår i: The First Sourcebook on Nordic Research in Mathematics Education, Norway, Sweden, Iceland, Denmark and contributions from Finland.. - Charlotte : Information Age Publishing.
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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| 4. |
- Silvestrov, Sergei
(författare)
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Interpolation of Normed Abelian Groups and Non-Commutative Integration
- 2012
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Ingår i: Analysis for Science, Engineering and Beyond. - Berlin : Springer Berlin/Heidelberg. - 9783642202353 ; , s. 325-341
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Bokkapitel (refereegranskat)abstract
- This is a concise review concerned first of all with the two pioneering far reaching and in many ways yet to be fully explored important papers by Gunnar Sparr and Jaak Peetre on interpolation of normed abelian groups and on non-commutative integration. These papers introduced a general framework unifying many previously known interpolation results and methods in the ways applicable for non-commutative integration and non-commutative extensions of the function spaces, the directions of importance for example in non-commutative geometry and applications in quantum physics. Whence some notions and methods from these papers have been applied in various contexts, many other methods and ideas are yet to be discovered and developed further. In addition to the concise review of these important works by Jaak Peetre and Gunnar Sparr, a brief review is presented also of some related works on non-commutative spaces and non-commutative integration in the contexts of the theory of operator algebras and non-commutative geometry
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| 5. |
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| 6. |
- Kiselman, Christer, 1939-
(författare)
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Frozen history : Reconstructing the climate of the past
- 2009
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Ingår i: Analysis, Partial Differential Equations and Applications. - Basel : Birkhäuser. - 9783764398972 ; , s. 97-114
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- The ice caps on Greenland and Antarctica are huge memory banks: the temperature of the past is preserved deep in the ice. In this paper we present a mathematical model for the reconstruction of past temperatures from records of the present ones in a drilled hole.
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| 7. |
- Pilipovic, Stevan, et al.
(författare)
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Singular Support and FL^q Continuity of Pseudodifferential Operators
- 2011
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Ingår i: Approximation and Computation. - New York, NY : Springer. ; , s. 365-383
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Bokkapitel (refereegranskat)abstract
- In this paper we show possible directions for numerical mathematicians interested in the approximation of different types of singular supports, wave front sets and of pseudodifferential operators in the framework of Fourier-Lebesgue spaces. The work contains new results on singular supports in Fourier-Lebesgue spaces and on the continuity properties of certain pseudodifferential operators.
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| 8. |
- Szulkin, Andrzej, et al.
(författare)
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The method of Nehari manifold
- 2010
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Ingår i: Handbook of Nonconvex Analysis and Applications. - Boston : International Press. - 9781571462008 ; , s. 597-632
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- We present a unified approach to the method of Nehari manifold for functionals which have a local minimum at 0 and we give several examples where this method is applied to the problem of finding ground states and multiple solutions for nonlinear elliptic boundary value problems. We also consider a recent generalization of this method to problems where 0 is a saddle point of the functional.
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