TY - JOUR AU - Hashemi Borzabadi, Akbar AU - Heidarian, Leila PY - 2011 TI - Determining the Objective Value Range for a Class of Interval Convex Optimization Problems JO - Journal of Mathematics and Computer Science SP - 396--402 VL - 3 IS - 4 AB - This paper generalizes a method of determining the objective value range of quadratic programming problems to a general class of interval convex programming ones, where all coefficients in objective function and constraints are interval numbers. The upper bound and lower bound of the objective values of the interval quadratic program is calculated by formulating a pair of two-level mathematical programs. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into conventional one-level convex programming problem. Solving the pair of convex programs produces the interval of the objective values of the problem. Numerical results confirms the procedure of the presented approach. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.03.04.05 DO - 10.22436/jmcs.03.04.05 ID - Hashemi Borzabadi2011 ER - TY - JOUR TI - An interval number programming approach for bilevel linear programming problem AU - S. A. Abass JO - International Journal of Management Science and Engineering Management PY - 2010 DA - 2010// VL - 5 ID - Abass2010 ER - TY - BOOK TI - Nonlinear Programming: Theory and Algorithm AU - M. S. Bazaraa AU - H. D. Sherali AU - C. M. Shetty PB - John Wiley & Sons PY - 1993 DA - 1993// CY - New York ID - Bazaraa1993 ER - TY - JOUR TI - An approach to interval programming problems with left-hand-side stochastic coefficients: An application to environmental decisions analysis AU - M. F. Cao AU - G. H. Huang AU - L. He JO - Expert Syst. Appl. PY - 2011 DA - 2011// VL - 38 ID - Cao2011 ER - TY - JOUR TI - Multiobjective programming in optimization of the interval objective function AU - H. Ishibuchi AU - H. Tanaka JO - Eur. J. Oper. Res. PY - 1990 DA - 1990// VL - 48 ID - Ishibuchi1990 ER - TY - JOUR TI - Ordering of Intervals and Optimization Problems with Interval Parameters AU - V. I. Levin JO - Cybernetics and Systems Analysis PY - 2004 DA - 2004// VL - 40 ID - Levin2004 ER - TY - JOUR TI - A class of linear interval programming problems and its application to portfolio selection AU - K. K. Lai AU - S. Y. Wang AU - J. P. Xu AU - S. S. Zhu AU - Y. Fang JO - IEEE Transactions on Fuzzy Systems PY - 2002 DA - 2002// VL - 10 ID - Lai2002 ER - TY - JOUR TI - Numerical solution method for general interval quadratic programming AU - W. Li AU - X. Tian JO - Applied Mathematics and Computation PY - 2008 DA - 2008// VL - 202 ID - Li2008 ER - TY - JOUR TI - A numerical solution method to interval quadratic programming AU - S.-T. Liu AU - R.-T. Wang JO - Applied Mathematics and Computation PY - 2007 DA - 2007// VL - 189 ID - Liu2007 ER - TY - JOUR TI - The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function AU - H.-C. Wu JO - Eur. J. Oper. Res. PY - 2007 DA - 2007// VL - 176 ID - Wu2007 ER - TY - JOUR TI - On interval-valued nonlinear programming problems AU - H. -C. Wu JO - J. Math. Anal. Appl. PY - 2008 DA - 2008// VL - 338 ID - Wu2008 ER -