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71.
Pierre Bonami Gérard Cornuéjols Sanjeeb Dash Matteo Fischetti Andrea Lodi 《Mathematical Programming》2008,113(2):241-257
Recent experiments by Fischetti and Lodi show that the first Chvátal closure of a pure integer linear program (ILP) often
gives a surprisingly tight approximation of the integer hull. They optimize over the first Chvátal closure by modeling the
Chvátal–Gomory (CG) separation problem as a mixed integer linear program (MILP) which is then solved by a general- purpose
MILP solver. Unfortunately, this approach does not extend immediately to the Gomory mixed integer (GMI) closure of an MILP,
since the GMI separation problem involves the solution of a nonlinear mixed integer program or a parametric MILP. In this
paper we introduce a projected version of the CG cuts, and study their practical effectiveness for MILP problems. The idea
is to project first the linear programming relaxation of the MILP at hand onto the space of the integer variables, and then
to derive Chvátal–Gomory cuts for the projected polyhedron. Though theoretically dominated by GMI cuts, projected CG cuts
have the advantage of producing a separation model very similar to the one introduced by Fischetti and Lodi, which can typically
be solved in a reasonable amount of computing time.
Gérard Cornuéjols was supported in part by NSF grant DMI-0352885, ONR grant N00014-03-1-0188, and ANR grant BLAN 06-1-138894.
Matteo Fischetti was supported in part by the EU projects ADONET (contract n. MRTN-CT-2003-504438) and ARRIVAL (contract n.
FP6-021235-2). Andrea Lodi was supported in part by the EU projects ADONET (contract n. MRTN-CT-2003-504438) and ARRIVAL (contract
n. FP6-021235-2). 相似文献
72.
Summary Cobaloxime complexes containing the biologically active ligand imidazole and poorly coordinating anions, such as ClO
4
–
or BF
4
–
, have been synthesised. The perchlorate anion is not involved in coordination and there is evidence that [Co(DH)2(L)2]ClO4 complexes are formed, whereas the tetrafluoroborate anion is involved in weak coordination giving complexes of the type [Co(DH)2(L)(BF4)] in the solid state. However, solvolysis of these latter complexes in solution yields 11 electrolytic species. The i.r. and electronic spectra, magnetic and conductivity measurements in nonaqueous media have been employed to characterise the complexes.Ligand abbreviations Py
pyridine
- Im
imidazole
- Me
methyl
- Al
allyl
- Vi
vinyl 相似文献
73.
Summary A series of manganese(II) spin-free complexes of the type: MnLn Cl2 [L =N-Methylimidazole (MeIm), n = 1,2,3,6; L =N-ethylimidazole (EtIm), n = 4], MnLnBr2 (L = MeIm, n = 2, 4, 6; L = EtIm, n = 4, 6), MnLnI2 (L = MeIm, n = 4, 6; L = EtIm, n = 6), MnLn(NCS)2 (L = MeIm, n = 3, 4; L = EtIm, n = 4), MnL6X2 (L = MeIm, EtIm; X = NO3, ClO4, BF4); (Me4N)(MnLCl3)(L = MeIm, EtIm); (Et4N)[Mn(MeIm)Br3] and Mn(MeIm)2(N3)2 · 5 H2O were prepared and characterized. The complexes have either octahedral, distorted octahedral, polymeric octahedral or tetrahedral structures. 相似文献
74.
A procedure for calculating critical exponents directly at finite ? is proposed. It relies on the invariance of the critical exponents at the critical coupling gc of the full theory with respect to finite changes in the renormalization point. This is expressed as the coincidence of curves at the point β = 0 in the plane of β versus a critical exponent parametrically described by the renormalized coupling for various values of the renormalization point (the “twisted fan”). If more than one critical exponent is present the fan is a set of curves in a multidimensional space with the twist at β = 0 and the exact values of the critical exponents. In perturbative approximations, an approximate invariance may result whether or not a zero of β exists to that order. We show that in the one and two loop approximations to the Reggeon calculus this approximate invariance does occur. The values of the critical exponents at the approximate twists show remarkable stability properties. We obtain σtot ≈ (lns)?γ where ?γ ≈ 0.11 and 0.17 for one and two loops respectively. 相似文献
75.
We apply the technique known in solid state physics as the n-loop expansion to calculate the critical indices of the φ3 Gribov Reggeon calculus directly in two transverse dimensions. Infrared pathologies of the massless theory require the calculation to be done in the infinite momentum limit of the massive theory. For n = 1 the results are close to those of the ε-expansion in O(ε). For n = 2 the β function has no zero, analogously to the case in solid state physics. Use of a Padé approximant for β yields σtot ≈ (1n s)0.27 at infinity, close to the O(ε2) result. 相似文献
76.
Chitta R. Panda Vivekananda Chakravortty Kailash C. Dash 《Transition Metal Chemistry》1988,13(4):287-290
Summary Interaction of ZrOCl2:8H2O, [Zr4(OH)8(H2O)16]Cl8 12H2O, with the heterocyclic, aldimines (PyAlA) and heterocyclic ketimines (AcPyA) in Me2CO in the presence of HC(OEt)3 yields white amorphous compounds of the type [Zr4(OH)12(H2O)8(PyAlA)2]Cl4 and [Zr4(OH)12(H2O)10(AcPyA)]Cl4. Presumably these compounds have a tetrameric dodecahedral structure, derived from the parent. The analytical data, i.r., electrical conductance and t.g. measurements all favour the tetrameric formulation. The t.g. studies also indicate the intermediacy of complex species, which lose water and the Schiff base ligands, with increase in temperature. 相似文献
77.
We calculate the ratios of πp, Kp and ψp total cross sections utilizing coupled homogeneous linear integral equations supplemented with SU(4) symmetry for the couplings. Kinematic effects arising from mass splitting and tmin effects are crucial. We obtain . 相似文献
78.
Reactions of PdL2 complexes, where LH = benzoylacetone, dibenzoyl methane, or dipivaloyl methane, with pyridine and neat β-diketones (L 1H trifluoroacetylacetone, hexafluoroacetylacetone, thenoyltrifluoroacetone and pivaloyltrifluoroacetone) in toluene resulted in the formation of central carbon (C3) bonded hetero-β-diketonate complexes of the formula [Pd(L)(C3-L′)py]. These were characterized by microanalyses, IR and 1H NMR spectral data. 相似文献
79.
Calorimetric and vapor pressure measurements of N2 monolayers on Grafoil have been made in the regions recently explored by neutron scattering. The phase transition at T = 48 K involves approximately symmetric specific heat anomalies of 2̃ K FWHM, and the peak position shifts about 1 K from to of one monolayer. In spite of the peak width and temperature shift the transition is intrinsically first order, due to melting of the √3 registered structure into a disordered phase in the presence of 2D vapor. The shift and broadening are shown to be a consequence of size effects primarily due to large edge-to-area ratios of the ordered phase domains. A formula relating the domain size to the shift in transition temperature gives r = 50' A for the mean radius of the domains. At film densities above monolayer the peak broadens and shifts to a higher temperature until a critical region is reached near T= 85 K. The combined heat capacity and vapor pressure data indicate that there is no two phase region at coverages near monolayer completion and that the transition near T = 85 K is higher than first order. Effects of molecular orientation and surface-normal vibration appear in certain regions of temperature and density. A phase diagram is constructed which is consistent with both calorimetric and neutron scattering results. 相似文献
80.
Dash K Thangavel S Krishnamurthy NV Rao SV Karunasagar D Arunachalam J 《The Analyst》2005,130(4):498-501
The speciation and determination of sulfate (SO4(2-)) and elemental sulfur (S degree) in zinc sulfide (ZnS) using ion-chromatography (IC) and reversed-phase liquid chromatography (RPLC) respectively is described. Three sample pretreatment approaches were employed with the aim of determining sulfate: (i) conventional water extraction of the analyte; (ii) solid-liquid aqueous extraction with an ultrasonic probe; and (iii) elimination of the zinc sulfide matrix via ion-exchange dissolution (IED). The separation of sulfate was carried out by an anion-exchange column (IonPac AS17), followed by suppressed conductivity detection. Elemental sulfur was extracted ultrasonically from the acid treated sample solution into chloroform and separated on a reversed phase HPLC column equipped with a diode array detector (DAD) at 264 nm. The achievable solid detection limits for sulfate and sulfur were 35 and 10 microg g(-1) respectively. 相似文献