On the efficiency of the algorithm for solving complex quadratic double–ratio minimax optimization problem

Zare, Arezu; Sadeghi Bigham, Bahram

doi:10.22034/cmde.2025.64854.2951

فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری

تعداد نشریات	45
تعداد شماره‌ها	1,468
تعداد مقالات	17,937
تعداد مشاهده مقاله	58,238,769
تعداد دریافت فایل اصل مقاله	19,709,591

	On the efficiency of the algorithm for solving complex quadratic double–ratio minimax optimization problem
Computational Methods for Differential Equations
مقاله 25، دوره 13، شماره 3، مهر 2025، صفحه 1074-1084 اصل مقاله (448.66 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.64854.2951
نویسندگان
Arezu Zare؛ Bahram Sadeghi Bigham^*
Department of Computer Science, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran.
چکیده
Quadratic fractional optimization problems frequently arise in wireless communications. This paper introduces an enhanced semidefinite optimization relaxation approach for tackling signal design challenges associated with quadratic double–ratio minimax optimization in complex space. It results in two algorithms that offer a global optimum solution for the problem.
کلیدواژه‌ها
Fractional programming؛ Minimax optimization؛ Quadratic programming؛ Semidefinite programming؛ Global optimization

مراجع
[1] . Beck and A. Ben–Tal, On the solution of the Tikhonov regularization of the total least squares problem, SIAM J. Optim., 17 (1) (2006), 98–118. [2] A. Beck and M. Teboulle, A convex optimization approach for minimizing the ratio of indefinite quadratic functions over an ellipsoid, Math. Program., 118(1) (2009), 13–35. [3] A. Beck, A. Ben–Tal, and M. Teboulle, Finding a global optimal solution for a quadratically constrained fractional quadratic problem with applications to the regularized total least squares, SIAM J. Matrix Anal. Appl., 28(2) (2006), 425–445. [4] A. Ben–Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms and Engineering Applications, SIAM, Philadelphia, 2001. [5] Y. Bresler and A. Macovski, Exact maximum likelihood parameter estimation of superimposed exponential signals in noise, IEEE Trans. Acust., Speech, Signal Process., 34(5) (1986), 1081–1089. [6] L. Consolini, M. Locatelli, J. Wang, and Y. Xia, Efficient local search procedures for quadratic fractional programming problems, Comput. Optim. Appl., 76 (2020), 201–232. [7] J. P. Crouzeix, J. A. Ferland, and S. Schaible, An algorithm for generalized fractional programs, J. Optim. Theory Appl., 47(1) (1985), 35–49. [8] J. P. Crouzeix, J. A. Ferland, and S. Schaible, A note on an algorithm for generalized fractional programs, J. Optim. Theory Appl., 50(1) (1986), 183–187. [9] M. Cui, G. Zhang, and R. Zhang, Secure wireless communication via intelligent reflecting surface, IEEE Wirel. Commun., 8(5) (2019), 1410–1414. [10] N. Datta and D. Bhatia, Duality for a class of nondifferentiable mathematical programming problems in complex space, J. Math. Anal. Appl., 101(1) (1984), 1–11. [11] G. Dartmann, X. Gong, W. Afzal, and G. Ascheid, On the duality of the max–min beamforming problem with per-antenna and per-antenna-array power constraints, IEEE Trans. Veh. Technol., 62(2) (2012), 606–619. [12] J. Flachs, Generalized Cheney–Loeb–Dinkelbach–type algorithms, Math. Oper. Res., 10(4) (1985), 674–687. [13] A. Gharanjik, M. R. B. Shankar, M. Soltanalian, and B. Ottersten, Max–min transmit beamforming via iterative regularization, in 50th Asilomar Conf. Signals, Systems & Computers, (2016), 1437–1441. [14] M. Grant and S. Boyd, Cvx: Matlab software for disciplined convex programming, Version 2.1, 2014. [15] P. C. Hansen, Regularization tools: a matlab package for analysis and solution of discrete ill–posed problems, Numer. Algorithms, 6(1) (1994), 1–35. [16] T. Y. Huang, Second-order parametric free dualities for complex minimax fractional programming, Mathematics, 8(1) (2020), 67-79. [17] E. Karipidis, N. D. Sidiropoulos, and Z. Q. Luo, Quality of service and max–min fair transmit beamforming to multiple cochannel multicast groups, IEEE Trans. Signal Process., 56(3) (2008), 1268–1279. [18] H. C. Lai and T. Y. Huang, Complex analysis methods related an optimization problem with complex variables, Eur. j. pure appl., 3(6) (2010), 989–1005. [19] H. C. Lai and J. C. Liu, Complex fractional programming involving generalized quasi/pseudo convex functions , J. Appl. Comput. Mech., 82(3) (2002), 159–166. [20] B. Tausiesakul and K. Asavaskulkiet, TDoA Localization in Wireless Sensor Networks Using Constrained Total Least Squares and Newton’s Methods, IEEE Access., 12 (2024), 39238–39260. [21] M. Schubert and H. Boche, Solution of the multiuser downlink beamforming problem with individual SINR constraints, IEEE Trans. Veh. Technol., 53(1) (2004), 18–28. [22] M. Shamailzadeh and A. H. Bastami, Cooperative beamforming in cognitive radio network with network–coded bidirectional filter–and–forward relaying, in Proc. ICEE, Shiraz, Iran, May, (2016), 1454–1459. [23] N. D. Sidiropoulos, T. N. Davidson, and Z.Q. Luo, Transmit beamforming for physical-layer multicasting, IEEE Trans. Signal Process., 54(6) (2006), 2239–2251. [24] V. P. Singh and A. K. Chaturvedi, Max–min fairness based linear transceiver–relay design for MIMO interference relay channel, IET Commun., 11(9) (2017), 1485–1496. [25] A. Zare, Solving the complex quadratic double-ratio minimax optimization under a quadratic constraint, J. Appl. Math., 69(1) (2023), 589–602. [26] A. Zare, A. Ashrafi, and Y. Xia, Quadratic double-ratio minimax optimization, Oper. Res. Lett., 49(4) (2021), 543–547. [27] A. Zhang and S. Hayashi, Celis–Dennis–Tapia based approach to quadratic fractional programming problems with two quadratic constraints, Numer. Algebra, Control and Optim., 1(1) (2011), 83–98.
آمار تعداد مشاهده مقاله: 373 تعداد دریافت فایل اصل مقاله: 359

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

On the efficiency of the algorithm for solving complex quadratic double–ratio minimax optimization problem