The approximate maximum and minimum amounts ofany phase in a complex mineral mixture can be determined by solving a linear programming problem involvingchemical mass balance and X-ray powder diffraction (XRD) data. Th...
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The approximate maximum and minimum amounts ofany phase in a complex mineral mixture can be determined by solving a linear programming problem involvingchemical mass balance and X-ray powder diffraction (XRD) data. The chemicalinformation necessary is the bulk composition ofthe mixture and an estimation of the compositional range of each of the minerals in the mixture. Stoichiometric constraints for the minerals may be used to reduce their compositional variation. Ifonly a partial chemical analysis for the mixture is available, the maximum amounts of the phases may still be estimated; however, some or all of the stoichiometric constraints may not apply. XRD measurements (scaled using an internal standard) may be incorporated into the linear programming problem using concentration-intensity re- lations between pairs of minerals. Each XRD constraint added to the linear programming problem, in general, reduces the difference between the calculated maximum and minimum amounts of each phase. Because it is necessary to define weights in the objective function of the linear programming problem, the proposed method must be considered a model. For many mixtures, however, the solution is relatively insensitive to the objective function weights. An example consisting of a mixture of montmorillonite, plagioclase feldspar, quartz, and opal-cristo- balite illustrates the linear programming approach. Chemical information alone was used to estimate the mineral abundances. Because quartz and opal-cristobalite are not chemicallydistinct, it was only possible to determine the sum, quartz + opal-cristobalite, present in the mixture.
In this paper, we give several results of learning errors for linear programming support vector regression. The corresponding theorems are proved in the reproducing kernel Hilbert space. With the covering number, the ...
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In this paper, we give several results of learning errors for linear programming support vector regression. The corresponding theorems are proved in the reproducing kernel Hilbert space. With the covering number, the approximation property and the capacity of the reproducing kernel Hilbert space are measured. The obtained result (Theorem 2.1) shows that the learning error can be controlled by the sample error and regularization error. The mentioned sample error is summarized by the errors of learning regression function and regularizing function in the reproducing kernel Hilbert space. After estimating the generalization error of learning regression function (Theorem 2.2), the upper bound (Theorem 2.3) of the regularized learning algorithm associated with linear programming support vector regression is estimated. Crown Copyright (C) 2010 Published by Elsevier Inc. All rights reserved.
We propose an entire space polynomial-time algorithm for linear programming. First, we give a class of penalty functions on entire space for linear programming by which the dual of a linear program of standard form ca...
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We propose an entire space polynomial-time algorithm for linear programming. First, we give a class of penalty functions on entire space for linear programming by which the dual of a linear program of standard form can be converted into an unconstrained optimization problem. The relevant properties on the unconstrained optimization problem such as the duality, the boundedness of the solution and the path-following lemma, etc, are proved. Second, a self-concordant function on entire space which can be used as penalty for linear programming is constructed. For this specific function, more results are obtained. In particular, we show that, by taking a parameter large enough, the optimal solution for the unconstrained optimization problem is located in the increasing interval of the self-concordant function, which ensures the feasibility of solutions. Then by means of the self-concordant penalty function on entire space, a path-following algorithm on entire space for linear programming is presented. The number ofNewton steps of the algorithm is no more than O(nL log(nL/epsilon)), and moreover, in short step, it is no more than O(root n log(nL/epsilon)).
Anaerobic co-digestion of multiple substrates has the potential to enhance biogas productivity by making use of the complementary characteristics of different substrates. A blending strategy based on a linear programm...
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Anaerobic co-digestion of multiple substrates has the potential to enhance biogas productivity by making use of the complementary characteristics of different substrates. A blending strategy based on a linear programming optimisation method is proposed aiming at maximising COD conversion into methane, but simultaneously maintaining a digestate and biogas quality. The method incorporates experimental and heuristic information to define the objective function and the linear restrictions. The active constraints are continuously adapted (by relaxing the restriction boundaries) such that further optimisations in terms of methane productivity can be achieved. The feasibility of the blends calculated with this methodology was previously tested and accurately predicted with an ADM1-based co-digestion model. This was validated in a continuously operated pilot plant, treating for several months different mixtures of glycerine, gelatine and pig manure at organic loading rates from 1.50 to 4.93 gCOD/L d and hydraulic retention times between 32 and 40 days at mesophilic conditions. (C) 2014 Elsevier Ltd. All rights reserved.
This paper presents a “standard form” variant of Karmarkar's algorithm for linear programming. The tecniques of using duality and cutting objective are combined in this variant to maintain polynomial-time comple...
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This paper presents a “standard form” variant of Karmarkar's algorithm for linear programming. The tecniques of using duality and cutting objective are combined in this variant to maintain polynomial-time complexity and to bypass the difficulties found in Karmarkar's original algorithm. The variant works with problems in standard form and simultaneously generates sequences of primal and dual feasible solutions whose objective function values converge to the unknown optimal value. Some computational results are also reported.
This paper presents a method for scheduling resources in complex systems that integrate humans with diverse hardware and software components, and for studying the impact of resource schedules on system characteristics...
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This paper presents a method for scheduling resources in complex systems that integrate humans with diverse hardware and software components, and for studying the impact of resource schedules on system characteristics. The method uses discrete-event simulation and integer linear programming, and relies on detailed models of the system's processes, specifications of the capabilities of the system's resources, and constraints on the operations of the system and its resources. As a case study, we examine processes involved in the operation of a hospital emergency department, studying the impact staffing policies have on such key quality measures as patient length of stay (LoS), number of handoffs, staff utilization levels, and cost. Our results suggest that physician and nurse utilization levels for clinical tasks of 70% result in a good balance between LoS and cost. Allowing shift lengths to vary and shifts to overlap increases scheduling flexibility. Clinical experts provided face validation of our results. Our approach improves on the state of the art by enabling using detailed resource and constraint specifications effectively to support analysis and decision making about complex processes in domains that currently rely largely on trial and error and other ad hoc methods.
Although nonnegative matrix factorization (NMF) is NP-hard in general, it has been shown very recently that it is tractable under the assumption that the input nonnegative data matrix is close to being separable. (Sep...
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Although nonnegative matrix factorization (NMF) is NP-hard in general, it has been shown very recently that it is tractable under the assumption that the input nonnegative data matrix is close to being separable. (Separability requires that all columns of the input matrix belong to the cone spanned by a small subset of these columns.) Since then, several algorithms have been designed to handle this subclass of NMF problems. In particular, Bittorf et al. [Adv. Neural Inform. Process. Syst., 25 (2012), pp. 1223-1231] proposed a linear programming model, referred to as Hottopixx. In this paper, we provide a new and more general robustness analysis of their method. In particular, we design a provably more robust variant using a postprocessing strategy which allows us to deal with duplicates and near duplicates in the data set.
The algorithm described here is a variation on Karmarkar’s algorithm for linear programming. It has several advantages over Karmarkar’s original algorithm. In the first place, it applies to the standard form of a li...
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The algorithm described here is a variation on Karmarkar’s algorithm for linear programming. It has several advantages over Karmarkar’s original algorithm. In the first place, it applies to the standard form of a linear programming problem and produces a monotone decreasing sequence of values of the objective function. The minimum value of the objective function does not have to be known in advance. Secondly, in the absence of degeneracy, the algorithm converges to an optimal basic feasible solution with the nonbasic variables converging monotonically to zero. This makes it possible to identify an optimal basis before the algorithm converges.
This paper discusses the transportation between China and America. The issues of trade nowadays involves many aspects of problems, from the basic quantity need of goods to the time requirement of different types of pr...
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In the gravitational method for linear programming, a particle is dropped from an interior point of the polyhedron and is allowed to move under the influence of a gravitational field parallel to the objective function...
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In the gravitational method for linear programming, a particle is dropped from an interior point of the polyhedron and is allowed to move under the influence of a gravitational field parallel to the objective function direction. Once the particle falls onto the boundary of the polyhedron, its subsequent motion is constrained to be on the surface of the polyhedron with the particle moving along the steepest-descent feasible direction at any instant. Since an optimal Vertex minimizes the gravitational potential, computing the trajectory of the particle yields an optimal solution to the linear program. Since the particle is not constrained to move along the edges of the polyhedron. as the simplex method does, the gravitational method seemed to have the promise of being theoretically more efficient than the simplex method. In this paper, we first show that, if the particle has zero diameter, then the worst-case time complexity of the gravitational method is exponential in the size of the input linear program. As a simple corollary of the preceding result, it follows that, even when the particle has a fixed nonzero diameter, the gravitational method has exponential time complexity. The complexity of the version of the gravitational method in which the particle diameter decreases as the algorithm progresses remains an open question.
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