zbMATH — the first resource for mathematics

D.C. programming approach for solving an applied ore-processing problem. (English) Zbl 1412.90120
Summary: This paper was motivated by a practical optimization problem formulated at the Erdenet Mining Corporation (Mongolia). By solving an identification problem for a chosen design of experiment we developed a quadratic model that quite adequately represents the experimental data. The problem obtained turned out to be the indefinite quadratic program, which we solved by applying the global search theory for a d.c. programming developed by A.S. Strekalovsky [in: Optimization in science and engineering. In honor of the 60th birthday of Panos M. Pardalos. New York, NY: Springer. 465–502 (2014; Zbl 1335.90075); Elements of nonconvex optimization. (Russian). Novosibirsk: Nauka (2003) ; Zh. Vychisl. Mat. Mat. Fiz. 43, No. 3, 399–409 (2003; Zbl 1103.26012); translation in Comput. Math. Math. Phys. 43, No. 3, 380–390 (2003)]. According to this d.c. optimization theory, we performed a local search that takes into account the structure of the problem in question, and constructed procedures of escaping critical points provided by the local search. The algorithms proposed for d.c. programming were verified using a set of test problems as well as a copper content maximization problem arising at the mining factory.

90C26 Nonconvex programming, global optimization
90C90 Applications of mathematical programming
90C20 Quadratic programming
Full Text: DOI
[1] R. Enkhbat and Ya. Bazarsad, General quadratic programming and its applications, in Optimization and optimal control (eds. A. Chinchuluun, P. M. Pardalos, R. Enkhbat and I. Tseveendorj), Springer-Verlag New York, (2010), 121-139. · Zbl 1204.90073
[2] R. Enkhbat; T. Ibaraki, Global optimization algorithms for general quadratic programming, J. Mong. Math. Soc., 5, 22, (2001) · Zbl 1232.90316
[3] T. V. Gruzdeva; A. S. Strekalovsky, Local search in problems with nonconvex constraints, Comput. Math. Math. Phys., 47, 381, (2007) · Zbl 1210.90134
[4] R. Horst; P. Pardalos; N. V. Thoai, Introduction to global optimization, Introduction to Global Optimization, , , (1995) · Zbl 0836.90134
[5] V. Jeyakumar; G. M. Lee; N. T. H. Linh, Generalized farkas lemma and gap-free duality for minimax dc optimization with polynomials and robust quadratic optimization, J. Global Optim., 64, 679, (2016) · Zbl 1346.90808
[6] V. Jeyakumar; A. M. Rubinov; Z. Y. Wu, Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions, Math. Program., 110, 521, (2007) · Zbl 1206.90178
[7] R. Horst; N. V. Thoai, D.C.programming: overview, J. Optim. Theory Appl., 103, 1, (1999) · Zbl 1073.90537
[8] R. H. Myers, Response Surface Methodology, Allyn and Bacon, Boston, MA, 1971.
[9] J. Nocedal and S. J. Wright, Numerical Optimization, Springer-Verlag, New York, 1999. · Zbl 0930.65067
[10] A. Rubinov, Abstract Convexity and Global Optimization, Springer US, Dordrecht, 2000. · Zbl 0985.90074
[11] A. M. Rubinov; Z. Y. Wu, Optimality conditions in global optimization and their applications, Math. Program., 120, 101, (2009) · Zbl 1191.90047
[12] A. S. Strekalovsky, On local search in d.c. optimization problems, Appl. Math. Comput., 255, 73, (2015) · Zbl 1338.90327
[13] A. S. Strekalovsky, On solving optimization problems with hidden nonconvex structures, in Optimization in science and engineering (eds. T. M. Rassias, C. A. Floudas and S. Butenko), Springer, New York, (2014), 465-502. · Zbl 1335.90075
[14] A. S. Strekalovsky, Elementy Nevypukloi Optimizatsii, (Russian) [Elements of nonconvex optimization], Nauka Publ., Novosibirsk, 2003.
[15] A. S. Strekalovsky, On the minimization of the difference of convex functions on a feasible set, Comput. Math. Math. Phys., 43, 380, (2003)
[16] A. S. Strekalovsky; A. A. Kuznetsova; T. V. Yakovleva, Numerical solution of nonconvex optimization problems, Numer. Anal. Appl., 4, 185, (2001) · Zbl 0997.90099
[17] A. S. Strekalovsky; T. V. Yakovleva, On a local and global search involved in nonconvex optimization problems, Autom. and Remote Control, 65, 375, (2004) · Zbl 1075.90062
[18] P. D. Tao; L. T. Hoai An, The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems, Ann. Oper. Res., 133, 23, (2005) · Zbl 1116.90122
[19] Z. Y. Wu; V. Jeyakumar; A. M. Rubinov, Sufficient conditions for global optimality of bivalent nonconvex quadratic programs with inequality constraints, J. Optim. Theory Appl., 133, 123, (2007) · Zbl 1144.90458
[20] Z. Y. Wu; A. M. Rubinov, Global optimality conditions for some classes of optimization problems, J. Optim. Theory Appl., 145, 164, (2010) · Zbl 1196.90099
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.