SDO and LDO relaxation approaches to complex fractional quadratic optimization

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.

[1]  Jen-Chwan Liu,et al.  Optimality and duality for complex nondifferentiable fractional programming , 1997 .

[2]  Henry Wolkowicz,et al.  Indefinite Trust Region Subproblems and Nonsymmetric Eigenvalue Perturbations , 1995, SIAM J. Optim..

[3]  C. R. Bector,et al.  A lagrangian approach to duality for complex nonlinear fractional programming over cones , 1977 .

[4]  Shuzhong Zhang,et al.  On Cones of Nonnegative Quadratic Functions , 2003, Math. Oper. Res..

[5]  N. Shor.  Dual quadratic estimates in polynomial and Boolean programming , 1991 .

[6]  M. Salahi,et al.  On fractional quadratic optimization problem with two quadratic constraints , 2020, Numerical Algebra, Control & Optimization.

[7]  Mustafa Cenk Gursoy,et al.  Relay beamforming strategies for physical-layer security , 2010, 2010 44th Annual Conference on Information Sciences and Systems (CISS).

[8]  H. Lai,et al.  Complex Fractional Programming Involving Generalized Quasi/Pseudo Convex Functions , 2002 .

[9]  Daniel Pérez Palomar,et al.  Fractional QCQP With Applications in ML Steering Direction Estimation for Radar Detection , 2011, IEEE Transactions on Signal Processing.

[10]  Alan F. Blackwell,et al.  Programming , 1973, CSC '73.

[11]  Siegfried Schaible,et al.  Fractional Programming , 2009, Encyclopedia of Optimization.

[12]  Xianfu Chen,et al.  Energy-Efficient Optimization for Wireless Information and Power Transfer in Large-Scale MIMO Systems Employing Energy Beamforming , 2013, IEEE Wireless Communications Letters.

[13]  Shuzhong Zhang,et al.  Complex Matrix Decomposition and Quadratic Programming , 2007, Math. Oper. Res..

[14]  Sean A. Ramprashad,et al.  Signal modeling and detection using cone classes , 1996, IEEE Trans. Signal Process..

[15]  Arkadi Nemirovski,et al.  Lectures on modern convex optimization - analysis, algorithms, and engineering applications , 2001, MPS-SIAM series on optimization.

[16]  Shahram Shahbazpanahi,et al.  Filter-and-Forward Distributed Beamforming in Relay Networks With Frequency Selective Fading , 2010, IEEE Transactions on Signal Processing.

[17]  Björn E. Ottersten,et al.  Collaborative-Relay Beamforming With Perfect CSI: Optimum and Distributed Implementation , 2009, IEEE Signal Processing Letters.

[18]  Adi Ben-Israel,et al.  A duality theorem for complex quadratic programming , 1969 .

[19]  Hoang Tuy,et al.  A Unified Monotonic Approach to Generalized Linear Fractional Programming , 2003, J. Glob. Optim..

[20]  Antonio De Maio,et al.  New Results on Fractional QCQP with Applications to Radar Steering Direction Estimation , 2014, IEEE Signal Processing Letters.

[21]  I. Stancu-Minasian.  Nonlinear Fractional Programming , 1997 .

[22]  Aharon Ben-Tal,et al.  Lectures on modern convex optimization , 1987 .

[23]  Shunsuke Hayashi,et al.  Celis-dennis-tapia based approach to quadratic fractional programming problems with two quadratic constraints , 2011 .

[24]  Wei Liu,et al.  Filter-and-forward distributed relay beamforming for cognitive radio systems , 2015, 2015 IEEE International Conference on Communication Workshop (ICCW).

[25]  Shu-Cherng Fang,et al.  KKT Solution and Conic Relaxation for Solving Quadratically Constrained Quadratic Programming Problems , 2011, SIAM J. Optim..

[26]  Werner Dinkelbach.  On Nonlinear Fractional Programming , 1967 .

[27]  Antonio De Maio,et al.  Adaptive Detection and Estimation in the Presence of Useful Signal and Interference Mismatches , 2009, IEEE Transactions on Signal Processing.

[28]  Sergiy A. Vorobyov,et al.  A Robust Adaptive Dimension Reduction Technique With Application to Array Processing , 2009, IEEE Signal Processing Letters.

[29]  Li Guo,et al.  Cooperative Beamforming in Cognitive Radio Network with Two-Way Relay , 2014, 2014 IEEE 79th Vehicular Technology Conference (VTC Spring).

[30]  John E. Mitchell,et al.  Using quadratic convex reformulation to tighten the convex relaxation of a quadratic program with complementarity constraints , 2014, Optim. Lett..

[31]  Yanfei Wang,et al.  An approach for minimizing a quadratically constrained fractional quadratic problem with application to the communications over wireless channels , 2014, Optim. Methods Softw..

[32]  Akiko Takeda,et al.  Successive Lagrangian relaxation algorithm for nonconvex quadratic optimization , 2018, Journal of Global Optimization.

[33]  James A. Ohlson,et al.  Portfolio Selection in a Lognormal Market When the Investor Has a Power Utility Function , 1976, Journal of Financial and Quantitative Analysis.

[34]  Y. Almogy,et al.  A Class of Fractional Programming Problems , 1971, Oper. Res..