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)).
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.
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.
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 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.
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 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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High mix-low volume operations face difficulties determining a specific order of processing, due to constant-changing market requirements and variability in processing times. Having an optimal and effective process fl...
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ISBN:
(纸本)9780983762447
High mix-low volume operations face difficulties determining a specific order of processing, due to constant-changing market requirements and variability in processing times. Having an optimal and effective process flow is essential for any manufacturing industry to meet customer requirements and revenue goals. linear programming and job sequencing techniques have been applied to determine the best sequence for processing group products. The constraints have been defined based in machine availability, production lot size, market demand, monthly revenue goals, and machines' capacity per type of product. The program selects the unit that enters the station comparing processing times and revenue, so that the waiting time between stations is minimized while simultaneously guaranteeing the revenue goal is fulfilled. The program have significantly reduced the cycle time and established effective sequences for every component to enter the production cycle. The total benefits have been maximized, the market demand has been attend, and the business goal in terms of revenue on deadline has been covered.
Semi-Markov decision processes on Borel spaces with deterministic kernels have many practical applications, particularly in inventory theory. Most of the results from general semi-Markov decision processes do not carr...
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Semi-Markov decision processes on Borel spaces with deterministic kernels have many practical applications, particularly in inventory theory. Most of the results from general semi-Markov decision processes do not carry over to a deterministic kernel since such a kernel does not provide "smoothness." We develop infinite dimensional linear programming theory for a general stochastic semi-Markov decision process. We give conditions, general enough to allow deterministic kernels, for solvability and strong duality of the resulting linear programs. By using the developed linear programming theory we give conditions for the existence of a stationary deterministic policy for deterministic kernels, which is optimal among all possible policies.
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