[1] | Strang, Gilbert, “Introduction to Applied Mathematics”, John Wiley & Sons Inc., New York, 1979. |
[2] | Strang, Gilbert, “Karmarkar’s algorithm and its place in applied mathematics”, The Msthematical Intelligencer 9(2): pp. 4-10, New York: Springer, 1987. |
[3] | Dantzig, G. G. “Maximization of a llinear function of variables subject to linear inequalities”, 1947, Published pp. 339-347, in T.C. Koopmans (ed.): Activity Analysis of Production and Allocation, Wiley & Chapman-Hall, New York-Lodon, 1951. |
[4] | Dantzig, G. B. “Linear Programming and Extensions”. Princeton, NJ: Princeton University Press, 1963. |
[5] | Fukuda, Komei and Terlaky, Tamas, “Crisis-cross methods: A fresh view on pivot algorithms”, Mathematical Programming: Series B, No. 79, Papers from 16th International Symposium on Mathematical Programming, Lausanne, 1997. |
[6] | Khachiyan, L. G., “Polynomial algorithms in linear programming”, U.S.S.R., Computational Mathematical and Mathematical Physics 20 (1980) pp. 53-72. |
[7] | Karmarkar, N., “A New Polynomial Time Algorithm for Linear Programming”, AT&T Bell Laboratories, Murray Hill, New Jersey, September, 1984. |
[8] | Gondzio, Jackek and Terlaky, Tamas, “A computational view of interior point method”, Advances in linear and integer programming, Oxford Lecture Series in Mathematics and its Applications, 4, New York, Osford University Press. pp. 103-144, MR1438311, 1996. |
[9] | Nocedal, Jorge and Wright, Stephen J,: “Numerical Optimization”, Springer Science+Business Media, Inc., 1999. |
[10] | Michael. R. Garey and David. S. Johnson, COMPUTERS AND INTRACTABILITY, A Guide to the Theory of NP-Completeness, Bell Laboratories, Murray Hill, New Jersey, 1979. |
[11] | Nemirovsky, A. and Yudin, N. “Interior-Point Polynomial Methods in Convex Programming”, Philadelphia, PA: SIAM, 1994. |
[12] | Alexander Schrijver, “Theory of Linear and Integer Programming”, Department of Econometrics”, Tilburg University, A Wiley-Interscience Publication, New York, 1979. |
[13] | Niedringhaus, W., “Stream Option Manager (SOM): Automated Integration of Aircraft Separation, Merging, Stream Management, and Other Air Traffic Control Problems”, IEEE Transactions Systems. Man & Cybernetics, Vol. 25 No. 9, Sept. 1995. |
[14] | Niedringhaus, W., “Maneuver Option Manager (MOM): Automated Simplification of Complex Air Traffic Control Problems”, IEEE Transactions Systems. Man & Cybernetics, May 1992. Niedringhaus, W., “Maneuver Option Manager (MOM): Automated Simplification of Complex Air Traffic Control Problems”, IEEE Transactions Systems. Man & Cybernetics, May 1992. |
[15] | Marcotte, Patrice, “A New Algorithm for Solving Variational Inequalties with Application to the Traffic Assignment Problem”, Centre de Recherche sur les Transports, University de Montreal, Canada, Mathematical Programming 33 (1985) pp. 339-351, North-Holland. |
[16] | Sun, Min, “A New Alternating Direction Method for Co-corecive Variational Inequality Problems with Linear Equality and Inequality Constraints”, pp. 161-176, Advanced Modeling and Optimization, Vol. 12, Number 2, 2010. |
[17] | Wang, Paul T. R., “Solving Linear Programming Problems in Self-dual Form with the Principle of Minmax”, MITRE MP-89W00023, The MITRE Corporation, July, 1989. |
[18] | Wang, Paul T. R., Niedringhaus, William P., and McMahon, Matthew T., “A Generic Linear Inequalities Solver (LIS) with an Application for Automated Air Traffic Control”. America Journal of Computational and Applied Mathematics, pp. 195-206, Volume 3, Number 4, August 2013, http://article.sapub.org/10.5923.j.ajcam.20130304.01.html |
[19] | Wang, Paul T. R., “Solving System of Linear Inequalities on the Surface of the Unit Shell (LIS-III)”. American Journal of Computational and Applied Mathematics, pp. 97-110, Volume 3, Number 4, August 2014, http://article.sapub.org/10.5923.j.ajcam.20140403.05.html. |
[20] | EE236-A, Lecture 15,” Self-dual formulations”, University of California, Department of Electrical Engineering, 2007-08. |
[21] | Self-DualForm:http://www.ee.ucla.edu/ee236a/lectures/hsd.pdf. |
[22] | ILOG, “Introduction to ILOG CPLEX”, 2007, http://www.ilog.com/products/optimization/qa.cfm?presentation=3. |
[23] | ILOG, “CPLEX Barrier Optimizer”, 2008, http://www.ilog.com/products/cplex/product/barrier.cfm. |
[24] | Steven Skiena, “LP_SOLVE: Linear Programming Code”, Stony Brook University, Dept. of Computer Science”, 2008 http://www.cs.sunysb.edu/~algorith/implement/lpsolve/implement.shtml. |
[25] | Deepmala, “A Study on Fixed Point Theorems for Nonlinear Contractions and its Applications”, Ph.D. Thesis (2014), Pt. Ravishankar Shukla University, Raipur (Chhatisgarh) India-492010. |
[26] | V.N. Mishra, “Some Problems on Approximations in Banach Spaces”, Ph.D. Thesis (2007), Indian Institute of Technology, Roorkee – 247 667, Uttarakhand, India. |
[27] | S. Husain, S. Gupta, V.N. Mishra; “An Existence Theoram of Solutions for the System of Generalized Vector Quasi-Variational-Like Inequalities”, American Journal of Operations Research (AJOR), 2013, 3.329-336. DOI:10.4236/AJOR.2013.22029. |
[28] | S. Husain, S. Gupta, V.N. Mishra; “Generalized H(.,.)--Cocoercive Operators and Generalized Set-Valued Variational-Like Inclusions”, Journal of Mathematics, Vol. 2013, Article3 ID 738491, 10 pages. |
[29] | S. Husain, S. Gupta, V.N. Mishra; “Graph Convergence for the H((.,.),(.,.))-Mixed Mapping with an Application for Solving the System of Genberalized Variational Inclusions” Fixed Point Theory and Applications 2013, 2013:304 DOI: 10.1186/1687-1812-2013-304. |