The main method of casting coal spontaneous combustion is prediction of index gases, with carbon monoxide(CO) commonly used as an index gas. However, coal spontaneous combustion is not the sole source of CO evolution;...The main method of casting coal spontaneous combustion is prediction of index gases, with carbon monoxide(CO) commonly used as an index gas. However, coal spontaneous combustion is not the sole source of CO evolution; primal CO is generated through coalification, which can lead to forecasting mistakes. Through theoretical analysis, primal CO generation and emission from coal seams was determined.In this study, six coal samples were analyzed under six different experimental conditions. The results demonstrated the change in coal seam primal gas and concentration as functions of time, different coal samples, occurrence, various gas types and composition concentration, which are in agreement with the previous study on primal CO generation. Air charging impacts on primal gas emission. Analysis of the experimental data with SPSS demonstrates that the relationship between primal CO concentration and time shows a power exponent distribution.展开更多
In this paper, we propose two new perturbation simplex variants. Solving linear programming problems without introducing artificial variables, each of the two uses the dual pivot rule to achieve primal feasibility, an...In this paper, we propose two new perturbation simplex variants. Solving linear programming problems without introducing artificial variables, each of the two uses the dual pivot rule to achieve primal feasibility, and then the primal pivot rule to achieve optimality. The second algorithm, a modification of the first, is designed to handle highly degenerate problems more efficiently. Some interesting results concerning merit of the perturbation are established. Numerical results from preliminary tests are also reported. [ABSTRACT FROM AUTHOR]展开更多
The training algorithm of classical twin support vector regression (TSVR) can be attributed to the solution of a pair of quadratic programming problems (QPPs) with inequality constraints in the dual space.However,this...The training algorithm of classical twin support vector regression (TSVR) can be attributed to the solution of a pair of quadratic programming problems (QPPs) with inequality constraints in the dual space.However,this solution is affected by time and memory constraints when dealing with large datasets.In this paper,we present a least squares version for TSVR in the primal space,termed primal least squares TSVR (PLSTSVR).By introducing the least squares method,the inequality constraints of TSVR are transformed into equality constraints.Furthermore,we attempt to directly solve the two QPPs with equality constraints in the primal space instead of the dual space;thus,we need only to solve two systems of linear equations instead of two QPPs.Experimental results on artificial and benchmark datasets show that PLSTSVR has comparable accuracy to TSVR but with considerably less computational time.We further investigate its validity in predicting the opening price of stock.展开更多
This study was conducted with the objective to determine carcass traits, meat yield, and primal meat cuts of Arsi, Harar, Jersey*Horro crossbred, and Ogaden cattle breeds at Haramaya University, Ethiopia. A total of 1...This study was conducted with the objective to determine carcass traits, meat yield, and primal meat cuts of Arsi, Harar, Jersey*Horro crossbred, and Ogaden cattle breeds at Haramaya University, Ethiopia. A total of 12 bulls of four cattle breeds (3 Arsi, 3 Harar, 3 F1 Jersey*Horro crossbred and 3 Ogaden) with almost similar ages were randomly assigned to four treatments in a completely randomised design (CRD). Data on carcass traits, meat yield, and primal meat cuts were analyzed using the General Linear Model (GLM) of the Statistical Analysis Software (SAS) 9.4 version. The overall averages of live body weight, hot carcass weight, chilled carcass weight, dressing percentages based on hot carcass weight, and rib eye area of experimental cattle breeds were 215.58 kg, 102.93 kg, 99.56 kg, 47.61%, and 8.13 inch<sup>2</sup>, respectively. The hot carcass weight and chilled carcass weight of the Ogaden (136.57;133.30 kg, resp.) breed were higher (p < 0.01) compared to other experimental cattle breeds. Dressing percentages based on hot carcass weight were higher (p < 0.05) for the Ogaden (49.61%) and Arsi (49.82%) cattle breeds compared to Harar and Jersey*Horro crossbred (45.73%, 45.27%, resp.) cattle breeds. The average meat yield and proportion of meat yield of cattle breeds were 77.52 kg and 77.46%, respectively. With a linear regression coefficient of prediction (R<sup>2</sup>) ranging from 52.26% to 93.58%, primal meat cuts significantly (p dicted meat yield. In conclusion, the breed of cattle had a significant (p 0.05) influence on live body weight, hot and chilled carcass weight, dressing percentage, rib eye area, subcutaneous fat thickness, meat yield, and the weights of most primal meat cuts. The Ogaden cattle breed had a higher and better meat yield, carcass traits, and most primal meat cuts compared to other experimental cattle breeds. Furthermore, the inclusion of corn silage in the diet of fattening bulls improved the carcass and meat yield. Therefore, the performance of Ogaden cattle compared to other a展开更多
In this article, we devise two dual based methods for obtaining very good solution to a single stage un-capacitated minimum cost flow problem. These methods are an improvement to the methods already developed by Sharm...In this article, we devise two dual based methods for obtaining very good solution to a single stage un-capacitated minimum cost flow problem. These methods are an improvement to the methods already developed by Sharma and Saxena [1]. We further develop a method to extract a very good primal solution from a given dual solution. We later demonstrate the efficacies and the significance of these methods on 150 random problems.展开更多
R. T. Rockafellar built a new general convex dual theory by introducing the conjugate function and the perturbation function. Following him, many other authors obtained some important results in generalized convex dua...R. T. Rockafellar built a new general convex dual theory by introducing the conjugate function and the perturbation function. Following him, many other authors obtained some important results in generalized convex dual programs and展开更多
This paper presents the dual specification of the least-squares method. In other words, while the traditional (primal) formulation of the method minimizes the sum of squared residuals (noise), the dual specification m...This paper presents the dual specification of the least-squares method. In other words, while the traditional (primal) formulation of the method minimizes the sum of squared residuals (noise), the dual specification maximizes a quadratic function that can be interpreted as the value of sample information. The two specifications are equivalent. Before developing the methodology that describes the dual of the least-squares method, the paper gives a historical perspective of its origin that sheds light on the thinking of Gauss, its inventor. The least-squares method is firmly established as a scientific approach by Gauss, Legendre and Laplace within the space of a decade, at the beginning of the nineteenth century. Legendre was the first author to name the approach, in 1805, as “méthode des moindres carrés”, a “least-squares method”. Gauss, however, used the method as early as 1795, when he was 18 years old. Again, he adopted it in 1801 to calculate the orbit of the newly discovered planet Ceres. Gauss published his way of looking at the least-squares approach in 1809 and gave several hints that the least-squares algorithm was a minimum variance linear estimator and that it was derivable from maximum likelihood considerations. Laplace wrote a very substantial chapter about the method in his fundamental treatise on probability theory published in 1812.展开更多
The range of optimal values in cost optimization models provides management with options for decision making. However, it can be quite challenging to achieve feasible range of optimality in Geometric programming (Gp) ...The range of optimal values in cost optimization models provides management with options for decision making. However, it can be quite challenging to achieve feasible range of optimality in Geometric programming (Gp) models having negative degrees of difficulty. In this paper, we conduct sensitivity analysis on the optimal solution of Geometric programming problem with negative degree of difficulty. Using imprest data, we determine the optimal objective function, dual decision variables, primal decision variables;the range of values, the cost coefficient and RHS constraint must lie for the solution to stay optimal. From the analysis, we established that incremental sensitivity analysis has the functional form .展开更多
The Maximum Likelihood method estimates the parameter values of a statistical model that maximizes the corresponding likelihood function, given the sample information. This is the primal approach that, in this paper, ...The Maximum Likelihood method estimates the parameter values of a statistical model that maximizes the corresponding likelihood function, given the sample information. This is the primal approach that, in this paper, is presented as a mathematical programming specification whose solution requires the formulation of a Lagrange problem. A result of this setup is that the Lagrange multipliers associated with the linear statistical model (where sample observations are regarded as a set of constraints) are equal to the vector of residuals scaled by the variance of those residuals. The novel contribution of this paper consists in deriving the dual model of the Maximum Likelihood method under normality assumptions. This model minimizes a function of the variance of the error terms subject to orthogonality conditions between the model residuals and the space of explanatory variables. An intuitive interpretation of the dual problem appeals to basic elements of information theory and an economic interpretation of Lagrange multipliers to establish that the dual maximizes the net value of the sample information. This paper presents the dual ML model for a single regression and provides a numerical example of how to obtain maximum likelihood estimates of the parameters of a linear statistical model using the dual specification.展开更多
This paper discusses a re-examinatlon of dual methods based on Gomory＇s cutting plane for the solution of the integer programming problem, in which the increment of objection function is allowed as a pivot variable t...This paper discusses a re-examinatlon of dual methods based on Gomory＇s cutting plane for the solution of the integer programming problem, in which the increment of objection function is allowed as a pivot variable to decide the search direction and stepsize. Meanwhile, we adopt the current equivalent face technique so that lattices are found in the discrete integral face and stronger valid inequalities are acquired easily.展开更多
In this paper, we prove the convergence of the nodal expansion method, a new numerical method for partial differential equations and provide the error estimates of approximation solution.
A primal-dual infeasible interior point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm. moving through the interior of polytope but not con...A primal-dual infeasible interior point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm. moving through the interior of polytope but not confining the iterates within the feasible region in our proposed algorithm result in a solution approach that is quite different and less sensitive to problem size, so providing the potential to dramatically improve the practical computation effectiveness.展开更多
In this article, we propose efficient methods for solving two stage transshipment problems. Transshipment problem is the special case of Minimum cost flow problem in which arc capacities are infinite. We start by prop...In this article, we propose efficient methods for solving two stage transshipment problems. Transshipment problem is the special case of Minimum cost flow problem in which arc capacities are infinite. We start by proposing a novel problem formulation for a two stage transshipment problem. Later, special structure of our problem formulation is utilized to devise two dual based heuristics solutions with computational complexity of O (n2), and O (n3) respectively. These methods are motivated by the methods developed by Sharma and Saxena [1], Sinha and Sharma [2]. Our methods differ in the initialization and the subsequent variation of the dual variables associated with the transshipment nodes along the shortest path. Lastly, a method is proposed to extract a very good primal solution from the given dual solutions with a computational complexity of O (n2). Efficacy of these methods is demonstrated by our numerical analysis on 200 random problems.展开更多
Dear editor,Primal-dual dynamics(PDD)and its variants are prominent first-order continuous-time algorithms to determine the primal and dual solutions of a constrained optimization problem(COP).Due to the simple struct...Dear editor,Primal-dual dynamics(PDD)and its variants are prominent first-order continuous-time algorithms to determine the primal and dual solutions of a constrained optimization problem(COP).Due to the simple structure,they have received widespread attention in various fields,such as distributed optimization[1],power systems[2],and wireless communication[3].In view of their wide applications,there are numerous theoretic studies on the convergence properties of PDD and its variants,including the exponential stability analysis[4]-[9].展开更多
基金provided by the National Natural Science Foundation of China(No.U1261214)
文摘The main method of casting coal spontaneous combustion is prediction of index gases, with carbon monoxide(CO) commonly used as an index gas. However, coal spontaneous combustion is not the sole source of CO evolution; primal CO is generated through coalification, which can lead to forecasting mistakes. Through theoretical analysis, primal CO generation and emission from coal seams was determined.In this study, six coal samples were analyzed under six different experimental conditions. The results demonstrated the change in coal seam primal gas and concentration as functions of time, different coal samples, occurrence, various gas types and composition concentration, which are in agreement with the previous study on primal CO generation. Air charging impacts on primal gas emission. Analysis of the experimental data with SPSS demonstrates that the relationship between primal CO concentration and time shows a power exponent distribution.
文摘In this paper, we propose two new perturbation simplex variants. Solving linear programming problems without introducing artificial variables, each of the two uses the dual pivot rule to achieve primal feasibility, and then the primal pivot rule to achieve optimality. The second algorithm, a modification of the first, is designed to handle highly degenerate problems more efficiently. Some interesting results concerning merit of the perturbation are established. Numerical results from preliminary tests are also reported. [ABSTRACT FROM AUTHOR]
基金supported by the National Basic Research Program (973) of China(No.2013CB329502)the National Natural Science Foundation of China(No.61379101)the Fundamental Research Funds for the Central Universities,China(No.2012LWB39)
文摘The training algorithm of classical twin support vector regression (TSVR) can be attributed to the solution of a pair of quadratic programming problems (QPPs) with inequality constraints in the dual space.However,this solution is affected by time and memory constraints when dealing with large datasets.In this paper,we present a least squares version for TSVR in the primal space,termed primal least squares TSVR (PLSTSVR).By introducing the least squares method,the inequality constraints of TSVR are transformed into equality constraints.Furthermore,we attempt to directly solve the two QPPs with equality constraints in the primal space instead of the dual space;thus,we need only to solve two systems of linear equations instead of two QPPs.Experimental results on artificial and benchmark datasets show that PLSTSVR has comparable accuracy to TSVR but with considerably less computational time.We further investigate its validity in predicting the opening price of stock.
文摘This study was conducted with the objective to determine carcass traits, meat yield, and primal meat cuts of Arsi, Harar, Jersey*Horro crossbred, and Ogaden cattle breeds at Haramaya University, Ethiopia. A total of 12 bulls of four cattle breeds (3 Arsi, 3 Harar, 3 F1 Jersey*Horro crossbred and 3 Ogaden) with almost similar ages were randomly assigned to four treatments in a completely randomised design (CRD). Data on carcass traits, meat yield, and primal meat cuts were analyzed using the General Linear Model (GLM) of the Statistical Analysis Software (SAS) 9.4 version. The overall averages of live body weight, hot carcass weight, chilled carcass weight, dressing percentages based on hot carcass weight, and rib eye area of experimental cattle breeds were 215.58 kg, 102.93 kg, 99.56 kg, 47.61%, and 8.13 inch<sup>2</sup>, respectively. The hot carcass weight and chilled carcass weight of the Ogaden (136.57;133.30 kg, resp.) breed were higher (p < 0.01) compared to other experimental cattle breeds. Dressing percentages based on hot carcass weight were higher (p < 0.05) for the Ogaden (49.61%) and Arsi (49.82%) cattle breeds compared to Harar and Jersey*Horro crossbred (45.73%, 45.27%, resp.) cattle breeds. The average meat yield and proportion of meat yield of cattle breeds were 77.52 kg and 77.46%, respectively. With a linear regression coefficient of prediction (R<sup>2</sup>) ranging from 52.26% to 93.58%, primal meat cuts significantly (p dicted meat yield. In conclusion, the breed of cattle had a significant (p 0.05) influence on live body weight, hot and chilled carcass weight, dressing percentage, rib eye area, subcutaneous fat thickness, meat yield, and the weights of most primal meat cuts. The Ogaden cattle breed had a higher and better meat yield, carcass traits, and most primal meat cuts compared to other experimental cattle breeds. Furthermore, the inclusion of corn silage in the diet of fattening bulls improved the carcass and meat yield. Therefore, the performance of Ogaden cattle compared to other a
文摘In this article, we devise two dual based methods for obtaining very good solution to a single stage un-capacitated minimum cost flow problem. These methods are an improvement to the methods already developed by Sharma and Saxena [1]. We further develop a method to extract a very good primal solution from a given dual solution. We later demonstrate the efficacies and the significance of these methods on 150 random problems.
文摘R. T. Rockafellar built a new general convex dual theory by introducing the conjugate function and the perturbation function. Following him, many other authors obtained some important results in generalized convex dual programs and
文摘This paper presents the dual specification of the least-squares method. In other words, while the traditional (primal) formulation of the method minimizes the sum of squared residuals (noise), the dual specification maximizes a quadratic function that can be interpreted as the value of sample information. The two specifications are equivalent. Before developing the methodology that describes the dual of the least-squares method, the paper gives a historical perspective of its origin that sheds light on the thinking of Gauss, its inventor. The least-squares method is firmly established as a scientific approach by Gauss, Legendre and Laplace within the space of a decade, at the beginning of the nineteenth century. Legendre was the first author to name the approach, in 1805, as “méthode des moindres carrés”, a “least-squares method”. Gauss, however, used the method as early as 1795, when he was 18 years old. Again, he adopted it in 1801 to calculate the orbit of the newly discovered planet Ceres. Gauss published his way of looking at the least-squares approach in 1809 and gave several hints that the least-squares algorithm was a minimum variance linear estimator and that it was derivable from maximum likelihood considerations. Laplace wrote a very substantial chapter about the method in his fundamental treatise on probability theory published in 1812.
文摘The range of optimal values in cost optimization models provides management with options for decision making. However, it can be quite challenging to achieve feasible range of optimality in Geometric programming (Gp) models having negative degrees of difficulty. In this paper, we conduct sensitivity analysis on the optimal solution of Geometric programming problem with negative degree of difficulty. Using imprest data, we determine the optimal objective function, dual decision variables, primal decision variables;the range of values, the cost coefficient and RHS constraint must lie for the solution to stay optimal. From the analysis, we established that incremental sensitivity analysis has the functional form .
文摘The Maximum Likelihood method estimates the parameter values of a statistical model that maximizes the corresponding likelihood function, given the sample information. This is the primal approach that, in this paper, is presented as a mathematical programming specification whose solution requires the formulation of a Lagrange problem. A result of this setup is that the Lagrange multipliers associated with the linear statistical model (where sample observations are regarded as a set of constraints) are equal to the vector of residuals scaled by the variance of those residuals. The novel contribution of this paper consists in deriving the dual model of the Maximum Likelihood method under normality assumptions. This model minimizes a function of the variance of the error terms subject to orthogonality conditions between the model residuals and the space of explanatory variables. An intuitive interpretation of the dual problem appeals to basic elements of information theory and an economic interpretation of Lagrange multipliers to establish that the dual maximizes the net value of the sample information. This paper presents the dual ML model for a single regression and provides a numerical example of how to obtain maximum likelihood estimates of the parameters of a linear statistical model using the dual specification.
基金Supported by the National Natural Science Foun-dation of China (70371032) the Doctor Educational Foundation ofthe Ministry of Education (20020486035)
文摘This paper discusses a re-examinatlon of dual methods based on Gomory＇s cutting plane for the solution of the integer programming problem, in which the increment of objection function is allowed as a pivot variable to decide the search direction and stepsize. Meanwhile, we adopt the current equivalent face technique so that lattices are found in the discrete integral face and stronger valid inequalities are acquired easily.
基金This project is supported by the National Science Foundation of China
文摘In this paper, we prove the convergence of the nodal expansion method, a new numerical method for partial differential equations and provide the error estimates of approximation solution.
基金Supported by the Doctoral Educational Foundation of China of the Ministry of Education(20020486035)
文摘A primal-dual infeasible interior point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm. moving through the interior of polytope but not confining the iterates within the feasible region in our proposed algorithm result in a solution approach that is quite different and less sensitive to problem size, so providing the potential to dramatically improve the practical computation effectiveness.
文摘In this article, we propose efficient methods for solving two stage transshipment problems. Transshipment problem is the special case of Minimum cost flow problem in which arc capacities are infinite. We start by proposing a novel problem formulation for a two stage transshipment problem. Later, special structure of our problem formulation is utilized to devise two dual based heuristics solutions with computational complexity of O (n2), and O (n3) respectively. These methods are motivated by the methods developed by Sharma and Saxena [1], Sinha and Sharma [2]. Our methods differ in the initialization and the subsequent variation of the dual variables associated with the transshipment nodes along the shortest path. Lastly, a method is proposed to extract a very good primal solution from the given dual solutions with a computational complexity of O (n2). Efficacy of these methods is demonstrated by our numerical analysis on 200 random problems.
文摘Dear editor,Primal-dual dynamics(PDD)and its variants are prominent first-order continuous-time algorithms to determine the primal and dual solutions of a constrained optimization problem(COP).Due to the simple structure,they have received widespread attention in various fields,such as distributed optimization[1],power systems[2],and wireless communication[3].In view of their wide applications,there are numerous theoretic studies on the convergence properties of PDD and its variants,including the exponential stability analysis[4]-[9].
