Strong optimal solutions of interval linear programming

Checking Strong Optimality of Interval Linear Programming

In this paper, we will discusse the strong optimality of general interval linear program (IvLP), that is, the IvLP has an optimal solution for each realization, and some necessary and sufficient conditions are established, based on the duality theory. Keywordsoptimal solution; strongly feasible; duality;

Optimal value range in interval linear programming

First step immersion in interval linear programming with linear dependencies

‎We consider a linear programming problem in a general form and suppose that all coefficients may vary in some prescribed intervals‎. ‎Contrary to classical models‎, ‎where parameters can attain any value from the interval domains independently‎, ‎we study problems with linear dependencies between the parameters‎. ‎We present a class of problems that are easily solved by reduction to the classi...

The optimal solution set of the interval linear programming problems

Determining the set of all optimal solutions of a linear program with interval data is one of the main problems discussed in interval optimization. We review two methods based on duality in linear programming, which are used to approximate the optimal set. Additionally, another decomposition method based on complementary slackness is proposed. This method provides the exact description of the o...

Satisficing solutions and duality in interval and fuzzy linear programming

In this paper, we introduce a class of fuzzy linear programming problems and de ne the concepts of feasible and satis cing solutions—the necessary tools for dealing with such problems. In this way, we show that the class of crisp (classical) LP problems can be embedded into the class of FLP ones. Moreover, for FLP problems we de ne the concept of duality and prove the weak and strong duality th...