The paper presents a novel camera calibration method using a two-step approach. First, a genetic algorithm is used to find a good enough approximation of the solution. Then a multidimensional unconstrained nonlinear m...
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The paper presents a novel camera calibration method using a two-step approach. First, a genetic algorithm is used to find a good enough approximation of the solution. Then a multidimensional unconstrained nonlinear minimization (Nelder-Mead simplex) algorithm is used to refine the solution. This approach avoids errors due to linearizations and. automatically finds a very good initial point for the error minimizing procedure. All the camera parameters (intrinsic and extrinsic) are determined simultaneously, giving a consistent solution. Tested on several cases, the proposed method proved to be an efficient tool for determining the camera parameters needed for various applications, like analytical photogrammetry, 3-D space reconstruction from 2-D images and vision-based head tracking.
This paper addresses an upper bound derived by Kitahara and Mizuno (Math Program A 137:579-586, 2013) on the number of basic feasible solutions of a linear program generated with the simplex algorithm. Their bound inc...
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This paper addresses an upper bound derived by Kitahara and Mizuno (Math Program A 137:579-586, 2013) on the number of basic feasible solutions of a linear program generated with the simplex algorithm. Their bound includes two parameters and , which are respectively the minimum and the maximum values of positive components in all basic feasible solutions. We show that is NP-hard to determine while can be computed in polynomial time. We also report some numerical results using alternative parameters for and gamma.
In this note, we show a mathematical error in paper ("An improved initial basis for the simplex algorithm" (Junior HV, Lins MPE. An improved initial basis for the simplex algorithm. Computers and Operations ...
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In this note, we show a mathematical error in paper ("An improved initial basis for the simplex algorithm" (Junior HV, Lins MPE. An improved initial basis for the simplex algorithm. Computers and Operations Research 2005;32: 1983-1993), and then offer a modified method using LU decomposition. Our preliminary computational results are very favorable. (C) 2006 Elsevier Ltd. All rights reserved.
An extension of the simplex algorithm is presented. For a given linear programming problem, a sequence of relaxed linear programming problems is solved until a solution to the original problem is reached. Each success...
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An extension of the simplex algorithm is presented. For a given linear programming problem, a sequence of relaxed linear programming problems is solved until a solution to the original problem is reached. Each successive relaxed problem is obtained from the previous one by adding a single constraint chosen from the constraints violated by the solution to the previous relaxed problem. This added constraint maximizes the cosine of the angle that the gradient of any violated constraint forms with the gradient of the objective function. In other words, each successive relaxed problem is obtained by adding the violated constraint most parallel to the objective function. The proposed algorithm terminates when no constraints are violated. Preliminary results indicate that this cosine simplex algorithm reduces both the number of simplex iterations and the number of computations at each iteration.
Solution of mechanical problems often requires the analytical or numerical calculation of equilibrium paths, while multidimensional solution sets are rare. From this requirement emerged numerous methods for the calcul...
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Solution of mechanical problems often requires the analytical or numerical calculation of equilibrium paths, while multidimensional solution sets are rare. From this requirement emerged numerous methods for the calculation of bifurcation diagrams. Two large groups of solution methods are the continuation methods and the scanning methods (however hybrid algorithm exists as well). The simplex algorithm is a robust approximative technique based on the Piecewise Linearization (PL)-algorithm, which has its application as a continuation and as a scanning algorithm as well. In this paper we will show the extension of the method for finding a 2-dimensional manifold (i.e. surface) with the scanning of the parameter space. We analyze the performance of the algorithm and its parallelization through two simple examples.
In this paper, the simplex algorithm and its variants are investigated. First, we de. ne a new concept called formal tableau, which leads to derive easily the dual solution from the latest primal table;without any dis...
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In this paper, the simplex algorithm and its variants are investigated. First, we de. ne a new concept called formal tableau, which leads to derive easily the dual solution from the latest primal table;without any distinction between the original variables and the slack ones. Second, we propose a new method for initializing the simplex algorithm. Unlike the two-phase and the big-M methods, our technique does not involve artificial variables. The computational results reveal that this new method is very favorable especially when the number of artificial variables is significant. Finally, this method will be combined with the notion of formal tableau leading naturally to a second new approach. (c) 2009 Elsevier Inc. All rights reserved.
A comparative analysis of the computational complexity of exact algorithms for estimating linear regression equations has been carried out using the least absolute deviations method. The aim of this study is to compar...
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A comparative analysis of the computational complexity of exact algorithms for estimating linear regression equations has been carried out using the least absolute deviations method. The aim of this study is to compare the computational efficiency of exact algorithms for descent along nodal straight lines and algorithms based on solving linear programming problems. To do that, the algorithm of gradient descent along nodal straight lines and algorithms for solving the equivalent primal and dual linear programming problems using the simplex method have been discussed. The computational complexity of the algorithms for implementing the least absolute deviation method in solving the primal and dual linear programming problems has been estimated. The average time for determining regression coefficients using the primal and dual linear programming problems and the average time for gradient descent along nodal straight lines have been compared in Monte Carlo statistical experiments. It is shown that both options are significantly inferior to the gradient descent along nodal straight lines in both the computational complexity of the algorithms and the computation time. The advantage of the algorithm for descent along nodal straight lines increases by two orders of magnitude or more with an increase in the sample size.
Recently, computational results demonstrated remarkable superiority of a so-called ＂largest-distance＂ rule and ＂nested pricing＂ rule to other major rules commonly used in practice, such as Dantzig＇s original rule...
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Recently, computational results demonstrated remarkable superiority of a so-called ＂largest-distance＂ rule and ＂nested pricing＂ rule to other major rules commonly used in practice, such as Dantzig＇s original rule, the steepest-edge rule and Devex rule. Our computational experiments show that the simplex algorithm using a combination of these rules turned out to be even more efficient.
The capacity to locate efficiently a subset of experimental conditions necessary for the identification of an operating envelope is a key objective in many studies. We have shown previously how this can be performed b...
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The capacity to locate efficiently a subset of experimental conditions necessary for the identification of an operating envelope is a key objective in many studies. We have shown previously how this can be performed by using the simplex algorithm and this paper now extends the approach by augmenting the established simplex method to form a novel hybrid experimental simplex algorithm (HESA) for identifying 'sweet spots' during scouting development studies. The paper describes the new algorithm and illustrates its use in two bioprocessing case studies conducted in a 96-well filter plate format. The first investigates the effect of pH and salt concentration on the binding of green fluorescent protein, isolated from Escherichia coli homogenate, to a weak anion exchange resin and the second examines the impact of salt concentration, pH and initial feed concentration upon the binding capacities of a FAb', isolated from E. coli lysate. to a strong cation exchange resin. Compared with the established algorithm. HESA was better at delivering valuable information regarding the size, shape and location of operating 'sweet spots' that could then be further investigated and optimized with follow up studies. To test how favorably these features of HESA compared with conventional DoE (design of experiments) methods, HESA results were also compared with approaches including response surface modeling experimental designs. The results show that HESA can return 'sweet spots' that are equivalently or better defined than those obtained from DoE approaches. At the same time the deployment of HESA to identify bioprocess-relevant operating boundaries was accompanied by comparable experimental costs to those of DoE methods. HESA is therefore a viable and valuable alternative route for identifying 'sweet spots' during scouting studies in bioprocess development. (C) 2012 Elsevier B.V. All rights reserved.
The simplex algorithm computes the simplex multipliers by solving a system (or two triangular systems) at each iteration. This note offers an efficient approach to updating the simplex multipliers in conjunction with ...
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The simplex algorithm computes the simplex multipliers by solving a system (or two triangular systems) at each iteration. This note offers an efficient approach to updating the simplex multipliers in conjunction with the Bartels-Golub and Forrest-Tomlin updates for LU factors of the basis. It only solves one triangular system. The approach was implemented within and tested against MINOS 5.51 on 129 problems from Netlib, Kennington and BPMPD. Computational results show that the new approach improves simplex implementations.
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