This paper examines a complex fractional quadratic optimization problem subject to two quadratic constraints. The original problem is transformed into a parametric quadratic programming problem by the well-known classical Dinkelbach method. Then a semidefinite and Lagrangian dual optimization approaches are presented to solve the nonconvex parametric problem at each iteration of the bisection and generalized Newton algorithms. Finally, the numerical results demonstrate the effectiveness of the proposed approaches.
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DOI : 10.1051/ro/2020090
Keywords: Fractional quadratic optimization, nonconvex problem, semidefinite programming, Lagrangian dual optimization
@article{RO_2021__55_S1_S2241_0,
author = {Ashrafi, Ali and Zare, Arezu},
title = {SDO and {LDO} relaxation approaches to complex fractional quadratic optimization},
journal = {RAIRO. Operations Research},
pages = {S2241--S2258},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
doi = {10.1051/ro/2020090},
mrnumber = {4223187},
zbl = {1472.90135},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2020090/}
}
TY - JOUR AU - Ashrafi, Ali AU - Zare, Arezu TI - SDO and LDO relaxation approaches to complex fractional quadratic optimization JO - RAIRO. Operations Research PY - 2021 SP - S2241 EP - S2258 VL - 55 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2020090/ DO - 10.1051/ro/2020090 LA - en ID - RO_2021__55_S1_S2241_0 ER -
%0 Journal Article %A Ashrafi, Ali %A Zare, Arezu %T SDO and LDO relaxation approaches to complex fractional quadratic optimization %J RAIRO. Operations Research %D 2021 %P S2241-S2258 %V 55 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2020090/ %R 10.1051/ro/2020090 %G en %F RO_2021__55_S1_S2241_0
Ashrafi, Ali; Zare, Arezu. SDO and LDO relaxation approaches to complex fractional quadratic optimization. RAIRO. Operations Research, Tome 55 (2021), pp. S2241-S2258. doi: 10.1051/ro/2020090
[1] and , A duality theorem for complex quadratic programming. J. Optim. Theory App. 4 (1969) 244–252. | MR | Zbl | DOI
[2] and , A class of fractional programming problems. Oper. Res. 19 (1971) 57–67. | MR | Zbl | DOI
[3] , and , Using quadratic convex reformulation to tighten the convex relaxation of a quadratic program with complementarity constraints. Optim. Lett. 8 (2014) 811–822. | MR | Zbl | DOI
[4] , and , A lagrangian approach to duality for complex nonlinear fractional programming over cones. Optimization 8 (1977) 17–25. | MR
[5] and , Lectures on Modern Convex Optimization. SIAM, Philadelphia, PA (2001). | MR | Zbl | DOI
[6] , and , An approach for minimizing a quadratically constrained fractional quadratic problem with application to the communications over wireless channels. Optim. Methods Softw. 29 (2014) 310–320. | Zbl | DOI
[7] , and , Filter-and-forward distributed beamforming in relay networks with frequency selective fading. IEEE Trans. Signal Process. 58 (2009) 1251–1262. | MR | Zbl | DOI
[8] , and , Energy-efficient optimization for wireless information and power transfer in large-scale mimo systems employing energy beamforming. IEEE Wireless Commun. Lett. 2 (2013) 667–670. | DOI
[9] , and , Programming, profit rates and pricing decisions. Acc. Rev. 44 (1969) 467–481.
[10] , Fractional Programming. Heldermann Verlag, Weinheim 4 (1988). | MR | Zbl
[11] , , , and , Adaptive detection and estimation in the presence of useful signal and interference mismatches. IEEE Trans. Signal Process. 57 (2008) 436–450. | MR | Zbl | DOI
[12] and , New results on fractional QCQP with applications to radar steering direction estimation. IEEE Signal Process. Lett. 21 (2014) 895–898. | DOI
[13] , , , and , Fractional QCQP with applications in ml steering direction estimation for radar detection. IEEE Trans. Signal Process. 59 (2010) 172–185. | MR | Zbl | DOI
[14] , On nonlinear fractional programming. Manage. Sci. 13 (1967) 492–498. | MR | Zbl | DOI
[15] and , Cvx: Matlab software for disciplined convex programming, version 2.1 (2014).
[16] and , A robust adaptive dimension reduction technique with application to array processing. IEEE Signal Process. Lett. 16 (2008) 22–25. | DOI
[17] and , Complex matrix decomposition and quadratic programming. Math. Oper. Res. 32 (2007) 758–768. | MR | Zbl | DOI
[18] and , Complex fractional programming involving generalized quasi/pseudo convex functions. ZAMM-J. Appl. Math. Mech./Z. Angew. Math. Mech. 82 (2002) 159–166. | MR | Zbl | DOI
[19] , and , Optimality and duality for complex nondifferentiable fractional programming. J. Math. Anal. App. 210 (1997) 804–824. | MR | Zbl | DOI
[20] , , , and , KKT solution and conic relaxation for solving quadratically constrained quadratic programming problems. SIAM J. Optim. 21 (2011) 1475–1490. | MR | Zbl | DOI
[21] , and , Filter-and-forward distributed relay beamforming for cognitive radio systems. In: 2015 IEEE International Conference on Communication Workshop (ICCW). IEEE (2015) 895–900.
[22] and , Optimal portfolio policies for an investor with a power utility function facing a log normal securities market. J. Financ. Quant. Anal 11 (1976) 1.
[23] and , A unified monotonic approach to generalized linear fractional programming. J. Global Optim. 26 (2003) 229–259. | MR | Zbl | DOI
[24] , A general method for solving extremal problems. In: Vol. 174 of Doklady Akademii Nauk. Russian Academy of Sciences, Doklady (1967) 33–36. | MR | Zbl
[25] , and , Signal modeling and detection using cone classes. IEEE Trans. Signal Process. 44 (1996) 329–338. | DOI
[26] , Dual quadratic estimates in polynomial and boolean programming. Ann. Oper. Res. 25 (1990) 163–168. | MR | Zbl | DOI
[27] and , Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations. SIAM J. Optim. 5 (1995) 286–313. | MR | Zbl | DOI
[28] and , On cones of nonnegative quadratic functions. Math. Oper. Res. 28 (2003) 246–267. | MR | Zbl | DOI
[29] and , Programming with linear fractional functionals in complex spaces. Cahiers du centre d’Etudes et de Recherche Operationelle 12 (1970) 103–109. | MR | Zbl
[30] and , Successive lagrangian relaxation algorithm for nonconvex quadratic optimization. J. Global Optim. 71 (2018) 313–339. | MR | Zbl | DOI
[31] , and , On fractional quadratic optimization problem with two quadratic constraints. Numer. Algebra Control Optim. 10 (2020) 301. | MR | Zbl | DOI
[32] and , Celis-dennis-tapia based approach to quadratic fractional programming problems with two quadratic constraints. Numer. Algebra Control Optim. 1 (2011) 83–98. | MR | Zbl | DOI
[33] and , Relay beamforming strategies for physical-layer security. In: 2010 44th Annual Conference on Information Sciences and Systems (CISS). IEEE (2010) 1–6.
[34] , , and , Cooperative beamforming in cognitive radio network with two-way relay. In: 2014 IEEE 79th Vehicular Technology Conference (VTC Spring). IEEE (2014) 1–5.
[35] , , and , Collaborative-relay beamforming with perfect CSI: Optimum and distributed implementation. IEEE Signal Process. Lett. 16 (2009) 257–260. | DOI
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