We consider the two-stage stochastic linear programming problem with quantile criterion in case when the vector of random parameters has a discrete distribution with a finite number of realizations. Based on the confi...
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We consider the two-stage stochastic linear programming problem with quantile criterion in case when the vector of random parameters has a discrete distribution with a finite number of realizations. Based on the confidence method and duality theorems, we construct a decompositional algorithm for finding guaranteeing solutions.
This paper proposes a linear programming approach for stabilization of positive Markovian jump systems (PMJSs) with a saturated single input. The proposed approach first derives a sufficient condition for stabilizatio...
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This paper proposes a linear programming approach for stabilization of positive Markovian jump systems (PMJSs) with a saturated single input. The proposed approach first derives a sufficient condition for stabilization of PMJSs with input saturation based on the linear co-positive Lyapunov function. By introducing an intermediate scalar whose absolute value is less than the absolute value of product of nonnegative vector of the linear co-positive Lyapunov function and input matrix and constructing a special form of the controller gains, this approach obtains a modified condition applicable for the linear programming. Finally, four numerical examples show that the proposed approach gives the larger domain of attraction than the existing approach based on the quadratic Lyapunov function. (C) 2018 Elsevier Ltd. All rights reserved.
When the simplex algorithm is used to calculate a linear programming (LP) problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will app...
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When the simplex algorithm is used to calculate a linear programming (LP) problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper. The principle of this method is to avoid choosing the row which the value of the element in the right side of constraint expression for LP in this row is zero as the row of the pivot element to make the matrix in LP density and ensure that most subsequent steps will improve the value of the objective function. One step following this principle is inserted in the existing LP algorithm to reselect the pivot element. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of LP problems as examples, the results indicate that this method can effectively improve the efficiency of LP for the sparse matrix.
Most of the applications related to security and biometric rely on skin region detection such as face detection, adult 3D objects filtering, and gesture recognition. In this paper, we propose a robust method for skin ...
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Most of the applications related to security and biometric rely on skin region detection such as face detection, adult 3D objects filtering, and gesture recognition. In this paper, we propose a robust method for skin detection on 3D coloured point clouds. Then, we extend this method to solve the problem of 3D face detection. To do so, we construct a weighted graph from initial coloured 3D point clouds. Then, we present a linear programming algorithm using a predictive model based on a data mining approach to classify and label graph vertices as skin and non-skin regions. Moreover, we apply some refinement rules on skin regions to confirm the presence of a face. Furthermore, we demonstrate the robustness of our method by showing and analysing some experimental results. Finally, we show that our method deals with many data that can be represented by a weighted graph such as 2D images and 3D models.
In this work, we relied on a particular exact method to solve NP-Hard problem of determining a horizontal fragmentation scheme in relational data warehouses. The method used is that of linear programming which is dist...
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In this work, we relied on a particular exact method to solve NP-Hard problem of determining a horizontal fragmentation scheme in relational data warehouses. The method used is that of linear programming which is distinguished by other methods by the existence of practical methods that facilitate the resolution of problems that may be described in linear form. We quote the Simplex method and the interior points. To meet the linearity of the objective function and constraints, we used initially "De Morgan" theorem, which is based on properties of sets to transform and optimize decision queries, from any form to a linear one. In addition to designing and solving the selection problem of horizontal fragmentation technique, we considered the problem in two simultaneous objectives, namely: the number of Inputs/Outputs needed to run the global workload, and number of fragments generated to identify the best solutions compared to the concept of Pareto dominance. In addition, to carry out our work, we used the Benchmark APB1 invoked by a workload, to achieve satisfactory results.
The final goal of the present paper is computing/estimating the calmness moduli from below and above of the optimal value function restricted to the set of solvable linear problems. Roughly speaking, these moduli prov...
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The final goal of the present paper is computing/estimating the calmness moduli from below and above of the optimal value function restricted to the set of solvable linear problems. Roughly speaking, these moduli provide measures of the maximum rates of decrease and increase of the optimal value under perturbations of the data (provided that solvability is preserved). This research is developed in the framework of (finite) linear optimization problems under canonical perturbations, i.e., under simultaneous perturbations of the right-hand side (RHS) of the constraints and the coefficients of the objective function. As a first step, part of the work is developed in the context of RHS pertubations only, where a specific formulation for the optimal value function is provided. This formulation constitutes the starting point in obtaining exact formulae/estimations for the corresponding calmness moduli from below and above. We point out the fact that all expressions for the desired calmness moduli are conceptually tractable (implementable) in so far as they are given exclusively in terms of the nominal data.
The advent of smart grids and active distribution networks has boosted the relevance of reliability in the operation and planning of distribution systems. As is customary, reliability is assessed analytically through ...
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The advent of smart grids and active distribution networks has boosted the relevance of reliability in the operation and planning of distribution systems. As is customary, reliability is assessed analytically through several standard indices. Unfortunately, analytical reliability assessment relies on simulation, thereby requiring the use of inexact heuristic- or metaheuristic-based solution methods to operate and plan distribution systems when economic and reliability criteria are jointly considered. In order to overcome this shortcoming, this paper presents a new optimization-based approach to compute the standard network-dependent reliability indices that are widely used in reliability-constrained distribution optimization models. As a major salient feature over the conventional simulation-based method, reliability indices are equivalently determined by an efficient approach based on linear programming, where the network topology is explicitly represented by decision variables of the optimization process. The proposed approach has been tested on several benchmarks including a 1080-node system. Numerical simulations show that the proposed approach yields the same results as the conventional algorithm. Moreover, the moderate computational effort is suitable for the subsequent integration of the proposed equivalent formulation in reliability-constrained optimization models for distribution operation and planning. Such successful numerical experience backs the potential of the proposed formulation to enable the use of sound techniques different from the available heuristics and metaheuristics to solve reliability-constrained operational and planning optimization models for distribution systems.
Arc-search interior-point methods have been proposed to capture the curvature of the central path using an approximation based on ellipse. Yang et al. (J Appl Math Comput 51(1-2):209-225, 2016) proved that an arc-sear...
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Arc-search interior-point methods have been proposed to capture the curvature of the central path using an approximation based on ellipse. Yang et al. (J Appl Math Comput 51(1-2):209-225, 2016) proved that an arc-search algorithm has the computational order of . In this paper, we propose an arc-search infeasible-interior-point algorithms and discuss its convergence analysis. We improve the polynomial bound from to , which is at least as good as the best existing bound for infeasible-interior-point algorithms for linear programming. Numerical results indicate that the proposed method solved LP instances faster than the existing method.
We review the simplex method and two interior-point methods (the affine scaling and the primal-dual) for solving linear programming problems for checking avoiding sure loss, and propose novel improvements. We exploit ...
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We review the simplex method and two interior-point methods (the affine scaling and the primal-dual) for solving linear programming problems for checking avoiding sure loss, and propose novel improvements. We exploit the structure of these problems to reduce their size. We also present an extra stopping criterion, and direct ways to calculate feasible starting points in almost all cases. For benchmarking, we present algorithms for generating random sets of desirable gambles that either avoid or do not avoid sure loss. We test our improvements on these linear programming methods by measuring the computational time on these generated sets. We assess the relative performance of the three methods as a function of the number of desirable gambles and the number of outcomes. Overall, the affine scaling and primal-dual methods benefit from the improvements, and they both outperform the simplex method in most scenarios. We conclude that the simplex method is not a good choice for checking avoiding sure loss. If problems are small, then there is no tangible difference in performance between all methods. For large problems, our improved primal-dual method performs at least three times faster than any of the other methods. (C) 2018 Elsevier Inc. All rights reserved.
In this paper a method is present solving fractional linear programming problems in fuzzy environment by ranging methods, where parameters are fuzzy numbers with uncertain coefficients in the objective function. Here ...
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In this paper a method is present solving fractional linear programming problems in fuzzy environment by ranging methods, where parameters are fuzzy numbers with uncertain coefficients in the objective function. Here we constitute the crisp relationship between the objective function and the decision variables to solve the resulting programming problem to find a fair optimal solution to the material related problem, illustrated with an example. (C) 2019 Elsevier Ltd. All rights reserved.
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