Geetanjali Panda

Efficient solution of interval optimization problem

In this paper the interval valued function is defined in the parametric form and its properties are studied. A methodology is developed to study the existence of the solution of a general interval optimization problem, which is expressed in terms of the interval valued functions. The methodology is applied to the interval valued convex quadratic programming problem.

Convex fuzzy mapping with differentiability and its application in fuzzy optimization

Abstract The concepts of differentiability, convexity, generalized convexity and minimization of a fuzzy mapping are known in the literature. The purpose of this present paper is to extend and generalize these concepts to fuzzy mappings of several variables using Buckley–Feuring approach for fuzzy differentiation and derive Karush–Kuhn–Tucker condition for the constrained fuzzy minimization problem.

A new solution method for fuzzy chance constrained programming problem

This paper deals with an optimization model, where both fuzziness and randomness occur under one roof. The concept of fuzzy random variable (FRV), mean and variance of FRV is used in the model. In particular, the methodology is developed in the presence of FRV in the constraint. The methodology is verified through numerical examples.

Solution of nonlinear interval vector optimization problem

In this paper a vector optimization problem is studied in uncertain environment.The objective functions and constraints of this problem are interval valued functions. Preferable efficient solution of the problem is defined and a methodology is developed to derive one preferable efficient solution. The proposed methodology is illustrated through a numerical example.

Sufficient optimality conditions and duality theory for interval optimization problem

This paper addresses the duality theory of a nonlinear optimization model whose objective function and constraints are interval valued functions. Sufficient optimality conditions are obtained for the existence of an efficient solution. Three type dual problems are introduced. Relations between the primal and different dual problems are derived. These theoretical developments are illustrated through numerical example.

A new methodology for crisp equivalent of fuzzy chance constrained programming problem

This paper deals with a chance constrained programming model, where both fuzziness and randomness are present in the objective function and constraints. The concept of fuzzy random variable, mean and variance of fuzzy random variable, minimum of fuzzy numbers are used in the model. The methodology is verified through a numerical example.

Equivalence class in the set of fuzzy numbers and its application in decision-making problems

An equivalence relation is defined in the set of fuzzy numbers. In a particular equivalence class, arithmetic operations of fuzzy numbers are introduced. A fuzzy matrix with respect to a particular class and its associated crisp matrices are also introduced. The concept of equivalence class is applied in fuzzy decision-making problems and justified through a numerical example.

An interval linear programming approach for portfolio selection model

Uncertainty plays an important role in predicting the future earning of the assets in the financial market and it is generally measured in terms of probability. But in some cases, it would be a good idea for an investor to state the expected returns on assets in the form of closed intervals. Therefore, in this paper, we consider a portfolio selection problem wherein expected return of any asset, risk level and proportion of total investment on assets are in the form of interval, and obtain an optimum (best) portfolio. Such portfolio gives the total expected return and proportion of total investment on assets in the form of interval. The proposed portfolio model is solved by considering an equivalent linear programming problem, where all the parameters of the objective function and constraints as well as decision variables are expressed in form of intervals. The procedure gives a strongly feasible optimal interval solution of such problem based on partial order relation between intervals. Efficacy of the results is demonstrated by means of numerical examples.

A modified Quasi-Newton method for vector optimization problem

In this paper, existence of critical point and weak efficient point of vector optimization problem is studied. A sequence of points in n-dimension is generated using positive definite matrices like Quasi-Newton method. It is proved that accumulation points of this sequence are critical points or weak efficient points under different conditions. An algorithm is provided in this context. This method is free from any kind of priori chosen weighting factors or any other form of a priori ranking or ordering information for objective functions. Also, this method does not depend upon initial point. The algorithm is verified in numerical examples.

Generalized quadratic programming problem with interval uncertainty

In this paper, a quadratic programming model is considered, wherein all parameters and decision variables take values in intervals. Existence of optimal solution for this model with certain acceptable level is justified and a methodology is proposed to derive such a solution. Finally, the theoretical development is illustrated by means of an example of portfolio selection.