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On unbounded and binary parameters in multi-parametric programming: applications to mixed-integer bilevel optimization and duality theory

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JOURNAL OF GLOBAL OPTIMIZATION 2017年第3期69卷 587-606页

作者： Oberdieck, Richard Diangelakis, Nikolaos A. Avraamidou, Styliani Pistikopoulos, Efstratios N. Imperial Coll London Ctr Proc Syst Engn Dept Chem Engn London England Texas A&M Univ Artie McFerrin Dept Chem Engn College Stn TX 77843 USA

In multi-parametric programming an optimization problem is solved as a function of certain parameters, where the parameters are commonly considered to be bounded and continuous. In this paper, we use the case of strictly convex multi-parametric quadratic programming (mp-QP) problems with affine constraints to investigate problems where these conditions are not met. Based on the combinatorial solution approach for mp-QP problems featuring bounded and continuous parameters, we show that (i) for unbounded parameters, it is possible to obtain the multi-parametric solution if there exists one realization of the parameters for which the optimization problem can be solved and (ii) for binary parameters, we present the equivalent mixed-integer formulations for the application of the combinatorial algorithm. These advances are combined into a new, generalized version of the combinatorial algorithm for mp-QP problems, which enables the solution of problems featuring both unbounded and binary parameters. This novel approach is applied to mixed-integer bilevel optimization problems and the parametric solution of the dual of a convex problem.

关键词： Unbounded problems binary parameters Multi-parametric programming Mixed-integer bilevel programming

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Isobaric vapor-liquid equilibria of 1-butanol-p-xylene system

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INTERNATIONAL JOURNAL OF THERMOPHYSICS 2006年第1期27卷 85-91页

作者： Rattan, V. K. Kapoor, Seema Singh, Sukhmehar Panjab Univ Dept Chem Engn & Technol Chandigarh 160014 India

Isobaric vapor-liquid equilibrium data were obtained for 1-butanol-p-xylene system at 97.3 kPa using a vapor recirculating type (modified Othmer's) equilibrium still. The activity coefficients were obtained by taking into consideration vapor-phase imperfections. The experimental data for this system were tested for thermodynamic consistency and were correlated by various equations. The system forms a minimum boiling azeotrope.

关键词： activity coefficients binary parameters 1-butanol equilibrium still p-xylene vapor-liquid equilibrium

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Estimation of solid solubilities in supercritical carbon dioxide: Peng-Robinson adjustable binary parameters in the near critical region

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FLUID PHASE EQUILIBRIA 2002年第1-2期203卷 111-132页

作者： Skerget, M Novak-Pintaric, Z Knez, Z Kravanja, Z Univ Maribor Fac Chem & Chem Engn SI-2000 Mariner Slovenia

The density dependence of the binary parameters of the Peng-Robinson equation of state in near the critical region was examined. Published solubility data of eight compounds in pure CO2 have been fitted to the Peng-Robinson equation in combination with one and two parameters van der Waals mixing rules and in combination with the three parameter density dependent mixing rule of Mohamed and Holder. A systematic study has been done to determine the influence of different terms in the mixing rules. In order to obtain density dependence, binary parameters were calculated for each isotherm at particular experimental point separately in the way to equalise experimental and calculated solubility data. The system was formulated as an equation-oriented model and solved by means of a nonlinear programming optimisation algorithm. For all compounds the binary interaction parameters thus obtained were found to vary strongly with pressure in the range from 75 bar to approximately 150 bar, i.e. near the critical end point (CEP) of the low temperature branch of the three phase solid-liquid-gas (SLG) curve. At higher pressures, the parameter is practically independent on pressure. In general, for the systems investigated, k(ij) increases linearly with increasing density and reaches a constant value at higher densities in the range from 700 to 800 kg/m(3), depending on the system under investigation. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： solid-fluid equilibria equation of state mixing rules binary parameters near critical region nonlinear programming

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Prediction of solubilities of complex medium-sized chemicals. II. Solutes in mixed solvents

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MOLECULAR SIMULATION 2004年第6期30卷 367-378页

作者： Abildskov, J O'Connell, JP Tech Univ Denmark Dept Chem Engn Comp Aided Proc Engn Ctr DK-2800 Lyngby Denmark Univ Virginia Dept Chem Engn Charlottesville VA 22904 USA

Our systematic approach for predicting the solubility of sparingly soluble solid fine chemicals and pharmaceuticals in pure solvents is extended to all compositions of fully miscible mixed solvents. Group contribution correlations are used for computing the difference in solubility at infinite dilution in the system of interest from an optimal reference solvent. The method minimizes the impact of uncertainties in pure-solute properties, decreases the number of adjustable parameters to be determined by data reduction, and suggests an efficient experimental strategy to find any unknown parameters. Several examples illustrate the method for mixed systems.

关键词： mixed solvents fugacity UNIFAC parameters binary parameters

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DISQUAC predictions on thermodynamic properties of ternary and higher multicomponent mixtures.: II.: Results for H^E of ternary mixtures containing nonpolar components, or one polar compound, two polar compounds, or one alcohol and hydrocarbons, or CCl₄

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CANADIAN JOURNAL OF CHEMISTRY-REVUE CANADIENNE DE CHIMIE 2001年第10期79卷 1447-1459页

作者： Gonzalez, JA Carmona, J Riesco, N de la Fuente, IG Cobos, JC Univ Valladolid Fac Ciencias Dept Termodinam & Fis Aplicada Valladolid Spain

The ability of the DISQUAC model for predicting excess enthalpies (H-E) of ternary systems on the basis of binary parameters only, i.e., neglecting ternary interactions is analyzed. At this end, DISQUAC results for a set of 95 ternary systems are examined. The solutions studied are formed by only hydrocarbons (or CCl4);or by one polar compound (not alcohols) and two hydrocarbons (or CCl4);or by two polar compounds (not alcohols) and one hydrocarbon (or CCl4);or by one alcohol and two hydrocarbons (or CCl4). Most of the H(E)s analyzed are endothermic, and valid at 298.15 K and atmospheric pressure. The mean deviation between experimental values and DISQUAC results is 5.5% for the ternary systems and 6.5% for the constituent binaries (181 mixtures). The interaction parameters used are valid for the description of thermodynamic properties of binary systems: vapor-liquid equilibria (VLE), liquid-liquid (LLE), and solid-liquid equilibria (SLE), H-E and excess heat capacities at constant pressure (C-p(E)), as well as H-E and VLE of ternary solutions. Predictions are, in most of the cases, independent of the mixture compounds, or the number of groups present in the system. Larger deviations underline typical shortcomings of the group contributions methods (e.g., Patterson's effect;branching). Note that results for the ternaries and for the constituent binaries are of the same order. This is not the case for the Dortmund version of UNIFAC. The mean deviations obtained using this model are 10.5% and 14% for the ternary and binary mixtures, respectively. Results from other models (original UNIFAC, Flory's theory, Nitta-Chao, UNIQUAC association model) for a number of systems are also compared to those obtained using DISQUAC.

关键词： predictions H-E ternary systems binary parameters geometrical methods Flory group contributions

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Thermodynamics of mixtures containing ethers.: PART II -: Isothermal x-y data for the ternary system MTBE plus methanol+1-butanol and for two constituent binaries:: DISQUAC predictions on VLE of ternary mixtures containing tertiary-alkyl ethers and organic solvents

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THERMOCHIMICA ACTA 2001年第2期373卷 161-171页

作者： González, JA Riesco, N de la Fuente, IG Cobos, JC Vergara, LA Cocero, MJ Univ Valladolid Fac Ciencias Dept Termodinam & Fis Aplicada GETEF Valladolid 47071 Spain Univ Valladolid Fac Ciencias Dept Ingn Quim Valladolid 47071 Spain

VLE data at 298.15 K (x-y measurements, where x and y are the mole fractions in liquid and vapor phase, respectively) for methanol or 1-butanol + methyl tert-butyl ether (MTBE) and for MTBE + methanol + 1-butanol systems are reported. These data and those available on literature on VLE at isothermal conditions for ternary systems containing tertiary-alkyl ethers (MTBE. tert-amyl methyl ether (TAME)) and organic solvents (hydrocarbons and 1-alkanols) are analyzed in terms of DISQUAC. The model correctly predicts VLE of this type of mixtures using binary parameters only, i.e. neglecting ternary interactions. Results are independent of the mixture considered. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： VLE ternary systems tertiary-alkyl ethers 1-alkanols binary parameters group contributions

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Salt effect on the enthalpy of mixing of water plus methanol at 303.15 K

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FLUID PHASE EQUILIBRIA 1999年第2期164卷 217-224页

作者： Kumar, MD Rajendran, M Anna Univ Alagappa Coll Technol Dept Chem Engn Chennai 600025 India

The excess enthalpy of the miscible water-methanol system has been measured at 303.15 K in an isothermal batch calorimeter with vapour space. The effect of the salts NH4Cl, CdCl2 and HgCl2 on H-E was studied. A decreasing trend in excess enthalpy for NH4Cl and HgCl2 but an increasing trend for CdCl2 with increasing salt concentrations have been observed. The experimental values of H-E have been correlated using a modified Redlich-Kister equation and the binary parameters have been estimated. The deviations were calculated and reported. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： salt effect enthalpy of mixing binary parameters

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GEQUAC, an excess Gibbs energy model describing associating and nonassociating liquid mixtures by a new model concept for functional groups

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FLUID PHASE EQUILIBRIA 1999年 158卷 381-389页

作者： Egner, K Gaube, J Pfennig, A Tech Univ Darmstadt Inst Chem Technol D-64287 Darmstadt Germany Rhein Westfal TH Aachen Lehrstuhl Therm Verfahrenstech A-52062 Aachen Germany

The physically founded excess Gibbs energy model, GEQUAC, allows the description of excess properties for associating as well as nonassociating liquid mixtures. This is achieved by explicitly accounting for different poles of molecular surface between which strong interactions take place in a mixture. In previous work, the model concept and the subsequent model equation were tested against results of Monte-Carlo computer simulations and proved the ability to describe g(E), h(E) and Ts-E of ketone + n-alkane and n-alcohol + n-alkane mixtures. This work provides model parameters fitted to binary isothermal VLE and hE data for the mixtures butanone + n-heptane, 1-butanol + n-heptane and butanone + 1-butanol as a first step in application. The model parameters show physical relevance and are used for prediction of isothermal VLE and hE data (own measurements) at 323 K of the ternary mixture butanone + n-heptane + 1-butanol. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： excess properties associating and nonassociating mixtures GEQUAC model group-contribution method binary parameters ternary data prediction

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GEQUAC, an excess Gibbs energy model describing associating and nonassociating liquid mixtures by a new model concept for functional groups

GEQUAC, an excess Gibbs energy model describing associating ...

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8th International Conference on Properties and Phase Equilibria for Product and Process Design

作者： Egner, K Gaube, J Pfennig, A Tech Univ Darmstadt Inst Chem Technol D-64287 Darmstadt Germany Rhein Westfal TH Aachen Lehrstuhl Therm Verfahrenstech A-52062 Aachen Germany

关键词： excess properties associating and nonassociating mixtures GEQUAC model group-contribution method binary parameters ternary data prediction

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Pitzer parameters for the pertechnetate ion in the system Na⁺/K⁺/Mg²⁺/Ca²⁺/Cl^-/SO₄^2-/TcO₄^-/H₂O at 25°C

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JOURNAL OF SOLUTION CHEMISTRY 1998年第2期27卷 107-120页

作者： Neck, V Konnecke, T Fanghanel, T Kim, JI Forschungszentrum Karlsruhe Inst Nukl Entsorgungstech D-76021 Karlsruhe Germany

Isopiestic vapor pressure experiments are performed at 25 degrees C with aqueous Mg(TcO4)(2) solutions and with ternary mixtures containing various combinations of NaTcO4, Mg(TcO4)(2), NaCl, MgCl2, Na2SO4, and MgSO4. The osmotic coefficients of the binary solutions are used to evaluate the binary Pitzer parameters beta((O)), beta((1)), and C-phi for Mg(TcO4)(2). We previously reported these parameters for NaTcO,. The binary parameters for KTcO4 and Ca(TcO4)(2) are evaluated from solubilities of KTcO4 in KCl and CaCl2 solutions, respectively. The mixing parameters theta(TcO4-/Cl-), psi(MTcO4-/Cl-), theta(TcO4-/SO42-), psi(M/TcO4-/SO42), and psi(Na+/Mg2+/TcO4-) are calculated from either osmotic coefficients or solubilities in the corresponding ternary mixtures. The evaluated set of Fitter parameters predicts well the activity coefficients and solubilities of KTcO4 in multicomponent systems.

关键词： sodium pertechnetate magnesium pertechnetate potassium pertechnetate osmotic coefficients activity coefficients solubility seawater system Pitzer model binary parameters mixing parameters

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