Một đánh giá về việc tính toán các giới hạn chính xác về mặt toán học cho các giá trị tối ưu của chương trình tuyến tính

Althaus, E., Dumitriu, D.: Certifying feasibility and objective value of linear programs. Op. Res. Lett. 40(4), 292–297 (2012) Applegate, D.L., Cook, W., Dash, S., Espinoza, D.G.: Exact solutions to linear programming problems. Op. Res. Lett. 35(6), 693–699 (2007) Audet, C., Hansen, P., Messine, F., Ninin, J.: The small octagons of maximal width. Discrete Comput. Geom. 49(3), 589–600 (2013) Baharev, A., Kolev, L., Rév, E.: Computing multiple steady states in homogeneous azeotropic and ideal two-product distillation. AIChE J. 57(6), 1485–1495 (2011) Baharev, A., Rév, E.: Reliable computation of equilibrium cascades with affine arithmetic. AIChE J. 54(7), 1782–1797 (2008) Benhamou, F., Granvilliers, L.: Chapter 16—continuous and interval constraints. Foundations of artificial intelligence. In: van Beek, P., Rossi, F., Walsh, T. (eds.) Handbook of Constraint Programming, vol. 2, pp. 571–603. Elsevier, New York (2006) Boccia, M., Sforza, A., Sterle, C., Vasilyev, I.: A cut and branch approach for the capacitated \(p\)-median problem based on Fenchel cutting planes. J. Math. Modell. Algorithms 7(1), 43–58 (2008) Chindelevitch, L., Trigg, J., Regev, A., Berger, B.: An exact arithmetic toolbox for a consistent and reproducible structural analysis of metabolic network models. Nat. Commun. 5(4893), 1–10 (2014) Cook, W., Dash, S., Fukasawa, R., Goycoolea, M.: Numerically safe gomory mixed-integer cuts. INFORMS J. Comput. 21(4), 641–649 (2009) Cook, W., Koch, T., Steffy, D.E., Wolter, K.: A hybrid branch-and-bound approach for exact rational mixed-integer programming. Math. Program. Comput. 5(3), 305–344 (2013) Cornuéjols, G., Margot, F., Nannicini, G.: On the safety of Gomory cut generators. Math. Program. Comput. 5(4), 345–395 (2013) Domes, F., Neumaier, A.: Rigorous filtering using linear relaxations. J. Glob. Optim. 53(3), 441–473 (2012) Fukasawa, R.: Gomory cuts. In: Cochran, J.J., Cox, L.A., Keskinocak, P., Kharoufeh, J.P., Cole Smith, J. (eds.) Wiley Encyclopedia of Operations Research and Management Science. Wiley, New York (2011) Gouttefarde, M., Daney, D., Merlet, J.-P.: Interval-analysis-based determination of the wrench-feasible workspace of parallel cable-driven robots. IEEE Trans. Robot. 27(1), 1–13 (2011) Guilbeau, J.T., Hossain, M.I., Karhbet, S.D., Kearfott, R.B., Sanusi, T.S., Zhao, L.: Advice for mathematically rigorous bounds on optima of linear programs. Technical report, University of Louisiana at Lafayette. http://interval.louisiana.edu/preprints/reformulations-for-rigorous (2016) Jansson, C.: Rigorous lower and upper bounds in linear programming. SIAM J. Optim. 14(3), 914–935 (2004) Jansson, C., Chaykin, D., Keil, C.: Rigorous error bounds for the optimal value in semidefinite programming. SIAM J. Numer. Anal. 46(1), 180–200 (2008) Jansson, C.: On verified numerical computations in convex programming. Jpn. J. Ind. Appl. Math. 26(2–3), 337–363 (2009) Jordan, N., Messine, F., Hansen, P.: 4OR. Reliab. Affine Relax. Method Glob. Optim. 13(3), 247–277 (2015) Kearfott, R.B.: Discussion and empirical comparisons of linear relaxations and alternate techniques in validated deterministic global optimization. Optim. Methods Softw. 21, 715–731 (2006) Kearfott, R.B., Castille, J., Tyagi, G.: GlobSol user guide. Optim. Methods Softw. 24(4–5), 687–708 (2009) Lebbah, Y., Michel, C., Rueher, M., Daney, D., Merlet, J.: Efficient and safe global constraints for handling numerical constraint systems. SIAM J. Numer. Anal. 42(5), 2076–2097 (2005) Lebbah, Y., Michel, C., Rueher, M.: A rigorous global filtering algorithm for quadratic constraints. Constraints 10(1), 47–65 (2005) Margot, F.: Testing cut generators for mixed-integer linear programming. Math. Program. Comput. 1(1), 69–95 (2009) Neumaier, A., Shcherbina, O., Huyer, W., Vinkó, T.: A comparison of complete global optimization solvers. Math. Program. 103(2), 335–356 (2005) Neumaier, A., Shcherbina, O.: Safe bounds in linear and mixed-integer programming. Math. Program. 99(2), 283–296 (2004) Porta, J.M., Ros, L., Thomas, F.: A linear relaxation technique for the position analysis of multiloop linkages. IEEE Trans. Robot. 25(2), 225–239 (2009) Prodan, I., Zio, E.: A model predictive control framework for reliable microgrid energy management. Int. J. Electr. Power Energy Syst. 61, 399–409 (2014) Ralph Baker, K., Castille, J., Tyagi, G.: A general framework for convexity analysis in deterministic global optimization. J. Glob. Optim. 56(3), 765–785 (2013) Ratschan, S., She, Z.: Providing a basin of attraction to a target region of polynomial systems by computation of Lyapunov-like functions. SIAM J. Control Optim. 48(7), 4377–4394 (2010) Smith, A.P.: Fast construction of constant bound functions for sparse polynomials. J. Glob. Optim. 43(2–3), 445–458 (2009) van Nooijen, R.R., Kolechkina, A.: Speed of discrete optimization solvers for real time sewer control. Urban Water J. 10(5), 354–363 (2013) Xiang, Y., Lan, T.: Smart Pricing Cloud Res. Wiley, New York (2014) Xuan-Ha, V., Sam-Haroud, D., Faltings, B.: Enhancing numerical constraint propagation using multiple inclusion representations. Ann. Math. Artif. Intell. 55(3–4), 295–354 (2009) Yi, X., Shunze, W., Zang, H., Hou, G.: An interval joint-probabilistic programming method for solid waste management: a case study for the city of Tianjin, China. Front. Environ. Sci. Eng. 8(2), 239–255 (2014)