Document Type: Research Paper
Authors
^{1} Department of Mathematics, Faculty of Basic Sciences, Gonbad Kavous University, Gonbad, Iran.
^{2} Department of Mathematics, Shahrood University of Technology, Shahrood, Iran.
Abstract
Keywords
Main Subjects
[1] Bazaraa, M. S., Sherali, H. D., & Shetty, C. M. (2013). Nonlinear programming: theory and algorithms. John Wiley & Sons.
[2] Beck, A., & Teboulle, M. (2000). Global Optimality conditions for quadratic optimization problems with binary constraints. SIAM journal on optimization, 11(1), 179-188.
[3] Das, S. K., & Mandal, T. (2017). A new model for solving fuzzy linear fractional programming problem with ranking function. Journal of applied research on industrial engineering, 4(2), 89-96.
[4] Ebrahimnejad, A., & LUIS, J. (2018). FUZZY SETS-BASED METHODS AND TECHNIQUES FOR MODERN ANALYTICS (Vol. 364). Springer International Publisher.
[5] Frasch, J. V., Sager, S., & Diehl, M. (2015). A parallel quadratic programming method for dynamic optimization problems. Mathematical programming computation, 7(3), 289-329.
[6] Gao, D. Y., & Ruan, N. (2010). Solutions to quadratic minimization problems with box and integer constraints. Journal of global optimization, 47(3), 463-484.
[7] Gill, P. E., & Wong, E. (2015). Methods for convex and general quadratic programming. Mathematical programming computation, 7(1), 71-112.
[8] Glover, F., Lü, Z., & Hao, J. K. (2010). Diversification-driven tabu search for unconstrained binary quadratic problems. 4OR, 8(3), 239-253.
[9] Goodarzi, F. K., Taghinezhad, N. A., & Nasseri, S. H. (2014). A new fuzzy approach to solve a novel model of open shop scheduling problem. University politehnica of bucharest scientific bulletin-series a-applied mathematics and physics, 76(3), 199-210.
[10] Hock, W., & Schittkowski, K. (1980). Test examples for nonlinear programming codes. Journal of optimization theory and applications, 30(1), 127-129.
[11] Jeyakumar, V., Rubinov, A. M., & Wu, Z. Y. (2007). Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions. Mathematical programming, 110(3), 521-541.
[12] Kao, C., & Liu, S. T. (2000). Fuzzy efficiency measures in data envelopment analysis. Fuzzy sets and systems, 113(3), 427-437.
[13] Kochenberger, G., Hao, J. K., Glover, F., Lewis, M., Lü, Z., Wang, H., & Wang, Y. (2014). The unconstrained binary quadratic programming problem: a survey. Journal of combinatorial optimization, 28(1), 58-81.
[14] Maros, I., & Mészáros, C. (1999). A repository of convex quadratic programming problems. Optimization methods and software, 11(1-4), 671-681.
[15] Molai, A. A. (2014). A new algorithm for resolution of the quadratic programming problem with fuzzy relation inequality constraints. Computers & industrial engineering, 72, 306-314.
[16] Molai, A. A. (2012). The quadratic programming problem with fuzzy relation inequality constraints. Computers & industrial engineering, 62(1), 256-263.
[17] Sun, X. L., Liu, C. L., Li, D., & Gao, J. J. (2012). On duality gap in binary quadratic programming. Journal of global optimization, 53(2), 255-269.
[18] Takapoui, R., Moehle, N., Boyd, S., & Bemporad, A. (2017). A simple effective heuristic for embedded mixed-integer quadratic programming. International journal of control, 1-11.
[19] Taleshian, F., & Fathali, J. (2016). A Mathematical Model for Fuzzy-Median Problem with Fuzzy Weights and Variables. Advances in operations research. http://dx.doi.org/10.1155/2016/7590492
[20] Taleshian, F., Fathali, J. & Taghi-Nezhad, N. A. (in press). Fuzzy majority algorithms for the 1-median and 2-median problems on a fuzzy tree. Fuzzy Information and Engineering.
[21] Xia, Y. (2009). New optimality conditions for quadratic optimization problems with binary constraints. Optimization letters, 3(2), 253-263.
[22] Zimmermann, H.J. (1986) Fuzzy Set Theory and Mathematical Programming. Fuzzy sets theory and applications, 99 -114.