Ajay Kumar Bhurjee

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.

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.

Optimal Range of Sharpe Ratio of a Portfolio Model with Interval Parameters

Abstract This paper proposes a Sharpe ratio portfolio optimization model wherein the expected return, variance and covariance of stocks vary in closed intervals. Objective function of this model is a nonlinear interval valued function. A solution methodology is developed for this model to obtain an efficient portfolio which provides the upper and lower bound of maximum value of the Sharpe ratio. The theoretical development is illustrated in a portfolio selection problem with historical data from the Indian Stock Market.

Multi-objective Optimization Problem with Bounded Parameters

In this paper, we propose a nonlinear multi-objective optimization problem whose parameters in the objective functions and constraints vary in between some lower and upper bounds. Existence of the efficient solution of this model is studied and gradient based as well as gradient free optimality conditions are derived. The theoretical developments are illustrated through numerical examples.

Optimal strategies for two-person normalized matrix game with variable payoffs

This paper considers a two-person zero-sum game model in which payoffs are varying in closed intervals. Conditions for the existence of saddle point for this model is studied in this paper. Further, a methodology is developed to obtain the optimal strategy for this game as well as the range of the corresponding optimal values. The theoretical development is verified through numerical example.

Solid transportation problem with budget constraints under interval uncertain environments

A solid transportation problem is formulated in the form of an interval linear programming problem, where transportation cost, availability, requirement, conveyance capacity and budget for destinations are represented as closed intervals. This problem is converted into a deterministic linear programming problem using some positive weight functions and establishes the relation between the solutions of both problems. Further, a novel methodology is developed to study the existence of solutions in interval solid transportation problems. Numerical example is illustrated to justify the efficiency of the proposed method.

Variational problems and its duality in banach spaces

Abstract The concept of duality for the variational problems is introduced in general Banach spaces. Different forms of duality such as Mangasarian and Mond-Weir type are studied. Mond-Weir type duality is considered to weaken the convexity requirements. Many duality (weak, strong and converse) results are established under generalized convexity assumptions. Again, examples and counterexamples are discussed in support of the investigation.AbstractThe concept of duality for the variational problems is introduced in general Banach spaces. Different forms of duality such as Mangasarian and Mond-Weir type are studied. Mond-Weir type duality is considered to weaken the convexity requirements. Many duality (weak, strong and converse) results are established under generalized convexity assumptions. Again, examples and counterexamples are discussed in support of the investigation.

Fractional Programming Problem with Bounded Parameters

In this paper, existence of the solution of a nonlinear fractional programming problem with parameters varying in some bounds, is studied. A general nonlinear programming problem, which is free from uncertain parameters, is formulated using the uncertain parameters of the original problem. Relation between the solution of the original problem and the transformed problem is established. The theoretical developments are justified in a numerical example.