A Survey on Grey Optimization

2018 ◽  
pp. 1-30
Author(s):  
Adem Guluma Negewo
Keyword(s):  
Linear Programming ◽  
Problem Solving ◽  
Quadratic Programming ◽  
Optimization Problems ◽  
Grey System Theory ◽  
Grey System ◽  
Work Area ◽  
Quadratic Programming Problems ◽  
General Nonlinear Programming ◽  
Future Work

This chapter provides a literature review of optimization problems in the context of grey system theory, as proposed by various authors. The chapter explains the binary interactive algorithm approach as a problem-solving method for linear programming and quadratic programming problems with uncertainty and a genetic-algorithm-based approach as a second problem-solving scheme for linear programming, quadratic programming, and general nonlinear programming problems with uncertainty. In the chapter, details on the computation procedures involved for solving the aforementioned optimization problems with uncertainty are presented and results from these two approaches are compared and contrasted. Finally, possible future work area in the subject is suggested.

A Survey on Grey Optimization

2021 ◽  
pp. 1260-1284
Author(s):  
Adem Guluma Negewo
Keyword(s):  
Linear Programming ◽  
Problem Solving ◽  
Quadratic Programming ◽  
Optimization Problems ◽  
Grey System Theory ◽  
Grey System ◽  
Work Area ◽  
Quadratic Programming Problems ◽  
General Nonlinear Programming ◽  
Future Work

This chapter provides a literature review of optimization problems in the context of grey system theory, as proposed by various authors. The chapter explains the binary interactive algorithm approach as a problem-solving method for linear programming and quadratic programming problems with uncertainty and a genetic-algorithm-based approach as a second problem-solving scheme for linear programming, quadratic programming, and general nonlinear programming problems with uncertainty. In the chapter, details on the computation procedures involved for solving the aforementioned optimization problems with uncertainty are presented and results from these two approaches are compared and contrasted. Finally, possible future work area in the subject is suggested.

A note on “a multi-objective programming approach to solve grey linear programming”

2018 ◽  
Vol 8 (1) ◽  
pp. 35-45 ◽  
Author(s):  
Amin Mahmoudi ◽  
Mohammad Reza Feylizadeh ◽  
Davood Darvishi
Keyword(s):  
Linear Programming ◽  
Linear Problem ◽  
Grey System Theory ◽  
Correct Solution ◽  
Programming Approach ◽  
Grey System ◽  
Content Type ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Linear Programming Problems

Purpose The purpose of this paper is to examine the shortcomings and problems associated with the method proposed by Razavi Hajiagha et al. (2012). Design/methodology/approach A multi-objective approach is proposed to solve the grey linear programming problems. In this method, the grey linear problem is converted into a multi-objective problem and then solved. Findings According to the numerical example presented in the study by Razavi Hajiagha et al. (2012), this method does not have a correct solution because the solution does not satisfy the constraints and the upper bounds of the variables are equal or less than their lower bound. Originality/value In recent years, various methods have been proposed for solving grey linear programming problems. Razavi Hajiagha et al. (2012) proposed a multi-objective approach to solve grey linear programming problems, but this method does not have a correct solution and using this method in other researches studies can reduce the value of the grey system theory.

scholarly journals On the relationship between regression analysis and mathematical programming

2004 ◽  
Vol 8 (2) ◽  
pp. 131-140 ◽  
Author(s):  
Dong Qian Wang ◽  
Stefanka Chukova ◽  
C. D. Lai
Keyword(s):  
Regression Analysis ◽  
Mathematical Programming ◽  
Quadratic Programming ◽  
Operations Research ◽  
Optimization Problems ◽  
The Other ◽  
Linear Quadratic ◽  
Quadratic Programming Problems ◽  
Simplex Methods ◽  
The Relationship

The interaction between linear, quadratic programming and regression analysis are explored by both statistical and operations research methods. Estimation and optimization problems are formulated in two different ways: on one hand linear and quadratic programming problems are formulated and solved by statistical methods, and on the other hand the solution of the linear regression model with constraints makes use of the simplex methods of linear or quadratic programming. Examples are given to illustrate the ideas.

scholarly journals An Algorithmic Technique for Solving Non-Linear Programming and Quadratic Programming Problems

2016 ◽  
Vol 35 ◽  
pp. 41-55
Author(s):  
HK Das ◽  
M Babul Hasan
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Graphical Representations ◽  
Computer Technique ◽  
Numerical Examples ◽  
Non Linear Programming ◽  
Non Linear ◽  
Quadratic Programming Problems ◽  
Algorithmic Technique ◽  
Combined Algorithm

In this paper, we improve a combined algorithm and develop a uniform computer technique for solving constrained, unconstrained Non Linear Programming (NLP) and Quadratic Programming (QP) problems into a single framework. For this, we first review the basic algorithms of convex and concave QP as well as general NLP problems. We also focus on the development of the graphical representations. We use MATHEMATICA 9.0 to develop this algorithmic technique. We present a number of numerical examples to demonstrate our method.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 41-55

Covered solution for a grey linear program based on a general formula for the inverse of a grey matrix

2014 ◽  
Vol 4 (1) ◽  
pp. 72-94 ◽  
Author(s):  
Qiao-Xing Li ◽  
Sifeng Liu ◽  
Nai-Ang Wang
Keyword(s):  
Linear Programming ◽  
Complex Systems ◽  
General Formula ◽  
Grey System Theory ◽  
Missing Information ◽  
Grey System ◽  
Content Type ◽  
The Matrix ◽  
Social Management ◽  
True Values

Purpose – This paper attempts to establish the general formula for computing the inverse of grey matrix, and the results are applied to solve grey linear programming. The inverse of a grey matrix and grey linear programming plays an important role in establishing a grey computational system. Design/methodology/approach – Starting from the fact that missing information often appears in complex systems, and therefore that true values of elements are uncertain when the authors construct a matrix, as well as calculate its inverse. However, the authors can get their ranges, which are called the number-covered sets, by using grey computational rules. How to get the matrix-covered set of inverse grey matrix became a typical approach. In this paper, grey linear programming was explained in detail, for the point of grey meaning and the methodology to calculate the inverse grey matrix can successfully solve grey linear programming. Findings – The results show that the ranges of grey value of inverse grey matrix and grey linear programming can be obtained by using the computational rules. Practical implications – Because the matrix and the linear programming have been widely used in many fields such as system controlling, economic analysis and social management, and the missing information is a general phenomenon for complex systems, grey matrix and grey linear programming may have great potential application in real world. The methodology realizes the feasibility to control the complex system under uncertain situations. Originality/value – The paper successfully obtained the ranges of uncertain inverse matrix and linear programming by using grey system theory, when the elements of matrix and the coefficients of linear programming are intervals and the results enrich the contents of grey mathematics.

scholarly journals A Procedure for Solving Quadratic Programming Problems

2017 ◽  
Vol 65 (1) ◽  
pp. 9-13
Author(s):  
HK Das
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Computer Technique ◽  
Quadratic Programming Problems ◽  
General Computer

In this paper, we study on the well-known procedure of quadratic programming (QP) and its corresponding linear programming (LP) problem. We then introduce a LP problem corresponding to the QP problem. Unfortunately, an unboundedness question arises into the new converting LP problem. We then modify the converted LP problem that overcomes the unboundedness. We introduce a general computer technique that can be solved the QP problem. An example is given to clarify the procedure and the computer technique. Dhaka Univ. J. Sci. 65(1): 9-13, 2017 (January)

SVM Soft Margin Classifiers: Linear Programming versus Quadratic Programming

2005 ◽  
Vol 17 (5) ◽  
pp. 1160-1187 ◽  
Author(s):  
Qiang Wu ◽  
Ding-Xuan Zhou
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Optimization Problems ◽  
Large Data ◽  
Misclassification Error ◽  
Support Vector ◽  
Svm Classifier ◽  
Classification Problems ◽  
Noise Condition ◽  
Soft Margin

Support vector machine (SVM) soft margin classifiers are important learning algorithms for classification problems. They can be stated as convex optimization problems and are suitable for a large data setting. Linear programming SVM classifiers are especially efficient for very large size samples. But little is known about their convergence, compared with the well-understood quadratic programming SVM classifier. In this article, we point out the difficulty and provide an error analysis. Our analysis shows that the convergence behavior of the linear programming SVM is almost the same as that of the quadratic programming SVM. This is implemented by setting a stepping-stone between the linear programming SVM and the classical 1-norm soft margin classifier. An upper bound for the misclassification error is presented for general probability distributions. Explicit learning rates are derived for deterministic and weakly separable distributions, and for distributions satisfying some Tsybakov noise condition.

scholarly journals A Proposed Technique for Solving Quasi-Concave Quadratic Programming Problems with Bounded Variables by Objective Separable Method

2016 ◽  
Vol 64 (1) ◽  
pp. 51-58
Author(s):  
M Asadujjaman ◽  
M Babul Hasan
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Objective Function ◽  
Programming Language ◽  
Optimal Solution ◽  
Linear Functions ◽  
Numerical Examples ◽  
Bounded Variables ◽  
Quadratic Programming Problems ◽  
Concave Quadratic Programming

In this paper, a new method namely, objective separable method based on Linear Programming with Bounded Variables Algorithm is proposed for finding an optimal solution to a Quasi-Concave Quadratic Programming Problems with Bounded Variables in which the objective function involves the product of two indefinite factorized linear functions and the constraint functions are in the form of linear inequalities. For developing this method, we use programming language MATHEMATICA. We also illustrate numerical examples to demonstrate our method.Dhaka Univ. J. Sci. 64(1): 51-58, 2016 (January)

scholarly journals Linear-quadratic programming and its application to data correction of improper linear programming problems

2020 ◽  
Vol 10 (1) ◽  
pp. 48-55
Author(s):  
Victor Gorelik ◽  
Tatiana Zolotova
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Linear Programming Problem ◽  
Optimization Problems ◽  
Lagrange Function ◽  
Frobenius Norm ◽  
Linear Quadratic ◽  
Quadratic Constraints ◽  
Linear Programming Problems ◽  
The Right

AbstractThe problem of maximizing a linear function with linear and quadratic constraints is considered. The solution of the problem is obtained in a constructive form using the Lagrange function and the optimality conditions. Many optimization problems can be reduced to the problem of this type. In this paper, as an application, we consider an improper linear programming problem formalized in the form of maximization of the initial linear criterion with a restriction to the Euclidean norm of the correction vector of the right-hand side of the constraints or the Frobenius norm of the correction matrix of both sides of the constraints.

Prediction of Technical Reserves Based on Grey Model — GM(1,1): Evidence from Non-life Egyptian Insurance Market

2019 ◽  
Vol 10 (9) ◽  
pp. 852-860
Author(s):  
Mahmoud Elsayed ◽  
◽  
Amr Soliman ◽  
Keyword(s):  
System Theory ◽  
Grey System Theory ◽  
Insurance Market ◽  
Grey Model ◽  
Loss Ratio ◽  
Grey System ◽  
Mathematical Technique ◽  
Supervisory Authority ◽  
Error Ratio ◽  
Using Data

Grey system theory is a mathematical technique used to predict data with known and unknown characteristics. The aim of our research is to forecast the future amount of technical reserves (outstanding claims reserve, loss ratio fluctuations reserve and unearned premiums reserve) up to 2029/2030. This study applies the Grey Model GM(1,1) using data obtained from the Egyptian Financial Supervisory Authority (EFSA) over the period from 2005/2006 to 2015/2016 for non-life Egyptian insurance market. We found that the predicted amounts of outstanding claims reserve and loss ratio fluctuations reserve are highly significant than the unearned premiums reserve according to the value of Posterior Error Ratio (PER).

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