Strong optimal solutions of interval linear programming

Abstract This paper considers optimal solutions of general interval linear programming problems. The new concepts of optimal solutions are introduced in a unified framework. Some existed optimal solution concepts of interval linear program such as weak and strong optimal solutions are special cases in this framework. Necessary and sufficient conditions for checking optimality are developed. Also, the features of the proposed methods are illustrated by some examples.

[1]  Shiang-Tai Liu,et al.  A numerical solution method to interval quadratic programming , 2007, Appl. Math. Comput..

[2]  Hsiao-Fan Wang,et al.  Decision Analysis of the Interval-Valued Multiobjective Linear Programming Problems , 2001 .

[3]  M. Hladík Optimal value bounds in nonlinear programming with interval data , 2011 .

[4]  Wei Li,et al.  Fault Detection in Discrete Dynamic Systems with Uncertainty Based on Interval Optimization , 2011 .

[5]  Milan Hladı´k Weak and strong solvability of interval linear systems of equations and inequalities , 2013 .

[6]  Milan Hladík,et al.  How to determine basis stability in interval linear programming , 2012, Optimization Letters.

[7]  Wei Li,et al.  Checking weak optimality of the solution to linear programming with interval right-hand side , 2014, Optim. Lett..

[8]  H. Ishibuchi,et al.  Multiobjective programming in optimization of the interval objective function , 1990 .

[9]  Wei Li,et al.  Numerical solution method for general interval quadratic programming , 2008, Appl. Math. Comput..

[10]  John W. Chinneck,et al.  Linear programming with interval coefficients , 2000, J. Oper. Res. Soc..

[11]  J. Rohn,et al.  Solvability of systems of interval linear equations and inequalities , 2006 .

[12]  Majid Soleimani-Damaneh,et al.  Optimal and strongly optimal solutions for linear programming models with variable parameters , 2007, Appl. Math. Lett..

[13]  L. Liu,et al.  An interval nonlinear program for the planning of waste management systems with economies-of-scale effects - A case study for the region of Hamilton, Ontario, Canada , 2006, Eur. J. Oper. Res..

[14]  Milan Hladík Optimal value range in interval linear programming , 2009, Fuzzy Optim. Decis. Mak..

[15]  Jiri Rohn,et al.  Strong solvability of interval linear programming problems , 1981, Computing.

[16]  Ralph E. Steuer Algorithms for Linear Programming Problems with Interval Objective Function Coefficients , 1981, Math. Oper. Res..