Method For Linear Programming Problems Research Articles

Penyelesaian Masalah Pemrograman Kuadratik Menggunakan Metode Beale

Quadratic programming is a special form of nonlinear programming which has the general form of the objective function in the form of a quadratic functions and the constraints in the form of linear functions. One of the methods used to solve the quadratic programming model is Beale’s method. This method is a modification of the simplex method for linear programming problems. This study aims to determine the optmal results of paddy production data in Balikpapan city using Beale’s method. The quadratic programming model was formed using the least squares method with the objective functions by selecting two types of plants,namely lowland paddy and upland paddy. Furthermore, the quadratic programming model formed that is formed is solved using Beale’s method. The data used is data on the paddy production of balikpapan city in 2005-2019. Based on the calculatios, the objective function is with the constraint functions and . After calculating using Beale’s method, the optimal result for the maximum yield of lowland paddy and upland paddy is quintals with a harvested area of hectares of lowland paddy and a harvested paddy of hectares of upland paddy.

Adaptive method of linear programming problems with hybrid variables

The principle of a constructing new algorithm of optimization for solution linear problems with hybrid variables is stated. It is an exact optimization method; a new improvement direction is proposed; criterion for suboptimal is proved. The results of the comparative numerical experiment by computer are presented.

Extension of Duality Results and a Dual Simplex Method for Linear Programming Problems With Intuitionistic Fuzzy Variables

The aim of this paper is to introduce a formulation of linear programming problems involving intuitionistic fuzzy variables. Here, we will focus on duality and a simplex-based algorithm for these problems. We classify these problems into two main different categories: linear programming with intuitionistic fuzzy numbers problems and linear programming with intuitionistic fuzzy variables problems. The linear programming with intuitionistic fuzzy numbers problem had been solved in the previous literature, based on this fact we offer a procedure for solving the linear programming with intuitionistic fuzzy variables problems. In methods based on the simplex algorithm, it is not easy to obtain a primal basic feasible solution to the minimization linear programming with intuitionistic fuzzy variables problem with equality constraints and nonnegative variables. Therefore, we propose a dual simplex algorithm to solve these problems. Some fundamental concepts and theoretical results such as basic solution, optimality condition and etc., for linear programming with intuitionistic fuzzy variables problems, are established so far. Moreover, the weak and strong duality theorems for linear programming with intuitionistic fuzzy variables problems are proved. In the end, the computational procedure of the suggested approach is shown by numerical examples.

A Distributed Method for Linear Programming Problems With Box Constraints and Time-Varying Inequalities

This letter proposes a multi-agent distributed solution for linear programming (LP) problems with time-invariant box constraints on the decision variables and possibly time-varying inequality constraints. This class of LP problems is relevant in different multi-agent smart systems. In the proposed approach, each agent computes only a single or a few of decision variables, while convergence to the optimal solution for the overall problem is guaranteed. Using a strong convexification of the problem combined with the barrier method, we prove that, despite the fact that the inequalities are time-varying, the tracking error remains bounded, and the bound is proportional to the rate of change of parameters. The effectiveness of the proposed scheme is demonstrated through a simulation study on a wireless power transfer network.

An efficient primal-dual interior point method for linear programming problems based on a new kernel function with a finite exponential-trigonometric barrier term

In this paper, we first propose a new finite exponential-trigonometric kernel function that has finite value at the boundary of the feasible region. Then by using some simple analysis tools, we show that the new kernel function has exponential convexity property. We prove that the large-update primal-dual interior-point method based on this kernel function for solving linear optimization problems has $$O\left( \sqrt{n}\log n\log \frac{n}{\epsilon }\right)$$ iteration bound in the worst case when the barrier parameter is taken large enough. Moreover, the numerical results reveal that the new finite exponential-trigonometric kernel function has better results than the other kernel functions.

Two-phase simplex method for linear semidefinite optimization

The linear semidefinite programming problem is considered. To solve it, the variant of the primal simplex method, that generalizes the corresponding method for linear programming problems, is proposed. The passage from one extreme point of the feasible set to another one is described. The main attention is given to pivoting in the case, when the extreme point is irregular, i.e. the “triangular” number of rank of the matrix in the basic point is less than number of equality type constraints in the problem. The approach for finding a starting extreme point is proposed too. The local convergence of the method is proven.

A Pivot Rule for Maximization Degeneracy Problems of Simplex Method for Linear Programming Problems

The simplex algorithm is a powerful technique, widely used to find the optimal solution of linear programming problems. Pivot rule is the most important first step of the simplex algorithm in the maximization degeneracy problems of LP for selecting the entering variable/work column (to obtain the smallest ratios) and after than leaving variable for pivot equation. The selection of an effective pivot rule leads the smallest number of iterations of the optimal solution of L.P. The selecting of most negative number (for entering variable) in the maximization problems is known as G.B Dantzig's pivot rule. The purpose of this paper is to model an algorithm that improves in the entering and leaving variable for the maximization degeneracy problems of LP. In this article, we have introduced a powerful technique for pivot rule which reduces the number of iterations to obtain the optimal solution as compare to Dantzig’s pivot rule. This article gives better concept of selection the entering variable as well leaving variable. This article also gives a helpful imminent into the unique and constructive performance of the proposed method by coverage computational experiments.

An Efficient Primal–Dual Interior Point Method for Linear Programming Problems Based on a New Kernel Function with a Trigonometric Barrier Term

In this paper, we present a primal---dual interior point method for linear optimization problems based on a new efficient kernel function with a trigonometric barrier term. We derive the complexity...

On the research of linear programming solving methods for non-hierarchical spare parts supply chain planning

Abstract: The relevance of planning non-hierarchical supply chains has increased due to growing collaboration among industrial and logistic organizations once this planning approach aims to optimize the supply chain while preserving each actor's individuality. Linear programming is the predominant modelling approach to deal with non-hierarchical supply chains according to the state-of-the-art literature. Metaheuristics and exact methods are the classical solving methods for linear programming problems, with different characteristics in terms of solution quality and capability of handling complex problems in feasible computation time. In this context, this paper evaluates methods to solve linear programming problems considering their capability of dealing with most common decision model types associated with spare parts supply chains applying collaborative planning concepts. The gathered references substantiate the conclusion that, for normal sized problems, the simplex method continues to be the most attractive method. For bigger problems, interior point methods can be a better alternative. And for problems that surpass interior point method capacity, metaheuristics are recommended.

Reduction-by-Projection Method for Linear Programming Problems

This paper defines the projection of algebic systems, and studies the projecting algorithm for linear systems. As its application, a new method is given to solve linear programming problems, which is called reduction-by-projection method. For many problems, especially when the problems have many constraint conditions in comparison with the number of their variables, the method needs less computation than simplex method and others. The great advantage of the method is shown when solving the integer linear programming problems.

Homotopy perturbation method for linear programming problems

In this paper, He’s homotopy perturbation method (HPM) is applied for solving linear programming (LP) problems. This paper shows that some recent findings about this topic cannot be applied for all cases. Furthermore, we provide the correct application of HPM for LP problems. The proposed method has a simple and graceful structure. Finally, a numerical example is displayed to illustrate the proposed method.

A bound for the number of different basic solutions generated by the simplex method

In this short paper, we give an upper bound for the number of different basic feasible solutions generated by the simplex method for linear programming problems (LP) having optimal solutions. The bound is polynomial of the number of constraints, the number of variables, and the ratio between the minimum and the maximum values of all the positive elements of primal basic feasible solutions. When the problem is primal nondegenerate, it becomes a bound for the number of iterations. The result includes strong polynomiality for Markov Decision Problem by Ye ( http://www.stanford.edu/~yyye/simplexmdp1.pdf , 2010) and utilize its analysis. We also apply our result to an LP whose constraint matrix is totally unimodular and a constant vector b of constraints is integral.

A primal-dual method for linear programming problems with fuzzy variables

Linear programming problems with fuzzy variables have been investigated by many researchers in the recent literature. Some methods to solve these problems, such as the primal simplex method and the dual simplex method, are based on the concept of comparison of fuzzy numbers by using ranking functions. In this paper, we give a new primal-dual algorithm for solving linear programming problems with fuzzy variables by using duality results, which was proposed by Mahdavi-Amiri and Nasseri (2007). This algorithm will be useful for sensitivity analysis when the activity vectors change for basic columns.

Adaptation-II of the surrogate methods for linear programming problems

Adaptation-II of the surrogate methods for linear programming problems

Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables

Linear programming problems with trapezoidal fuzzy variables (FVLP) have recently attracted some interest. Some methods have been developed for solving these problems by introducing and solving certain auxiliary problems. Here, we apply a linear ranking function to order trapezoidal fuzzy numbers. Then, we establish the dual problem of the linear programming problem with trapezoidal fuzzy variables and hence deduce some duality results. In particular, we prove that the auxiliary problem is indeed the dual of the FVLP problem. Having established the dual problem, the results will then follow as natural extensions of duality results for linear programming problems with crisp data. Finally, using the results, we develop a new dual algorithm for solving the FVLP problem directly, making use of the primal simplex tableau. This algorithm will be useful for sensitivity (or post optimality) analysis when using primal simplex tableaus.

Parabolic target space and primal–dual interior-point methods

In this paper we develop new primal–dual interior-point methods for linear programming problems, which are based on the concept of parabolic target space. We show that such schemes work in the infinity-neighborhood of the primal–dual central path. Nevertheless, these methods possess the best known complexity estimate. We demonstrate that the adaptive-step path-following strategies can be naturally incorporated in such schemes.

Rounding of convex sets and efficient gradient methods for linear programming problems

In this paper, we propose new efficient gradient schemes for two non-trivial classes of linear programming problems. These schemes are designed to compute approximate solutions with relative accuracy δ. We prove that the upper complexity bound for both schemes is O((√(n ln m)/δ)ln n) iterations of a gradient-type method, where n and m (n<m) are the sizes of the corresponding linear programming problems. The proposed schemes are based on preliminary computation of an ellipsoidal rounding for some polytopes in R n . In both cases, this computation can be performed very efficiently, in O(n 2 m ln m) operations at most.

Algorithm 836

Two codes are discussed, COLAMD and SYMAMD, that compute approximate minimum degree orderings for sparse matrices in two contexts: (1) sparse partial pivoting, which requires a sparsity preserving column pre-ordering prior to numerical factorization, and (2) sparse Cholesky factorization, which requires a symmetric permutation of both the rows and columns of the matrix being factorized. These orderings are computed by COLAMD and SYMAMD, respectively. The ordering from COLAMD is also suitable for sparse QR factorization, and the factorization of matrices of the form A T A and AA T , such as those that arise in least-squares problems and interior point methods for linear programming problems. The two routines are available both in MATLAB and C-callable forms. They appear as built-in routines in MATLAB Version 6.0.

Rounding of Convex Sets and Efficient Gradient Methods for Linear Programming Problems

In this paper we propose new efficient gradient schemes for two non-trivial classes of linear programming problems. These schemes are designed to compute approximate solutions with relative accuracy [delta]. We prove that the upper complexity bound for both schemes is O(([square root]n.ln.m)/[delta].ln.n) iterations of a gradient-type method, where n and m, (n

Mean value cross decomposition applied to integer programming problems

The mean value cross decomposition method for linear programming problems is a modification of ordinary cross decomposition, that eliminates the need for using the Benders or Dantzig-Wolfe master problems. As input to the dual subproblem the average of a part of all known dual solutions of the primal subproblem is used, and as input to the primal subproblem the average of a part of all known primal solutions of the dual subproblem. In this paper we study the lower bounds on the optimal objective function value of (linear) pure integer programming problems obtainable by the application of mean value cross decomposition, and find that this approach can be used to get lower bounds ranging from the bound obtained by the LP-relaxation to the bound obtained by the Lagrangean dual. We examplify by applying the technique to the clustering problem and give some preliminary computational results.