Power allocations in an interference-limited wireless network for global maximization of the weighted sum throughput or global optimization of the minimum weighted rate among network links are not only important but also very hard optimization problems due to their nonconvexity nature. Recently developed methods are either unable to locate the global optimal solutions or prohibitively complex for practical applications. This paper exploits the d.c. (difference of two convex functions/sets) structure of either the objective function or constraints of these global optimization problems to develop efficient iterative algorithms with very low complexity. Numerical results demonstrate that the developed algorithms are able to locate the global optimal solutions by only a few iterations and they are superior to the previously-proposed methods in both performance and computation complexity.

Fast Global Optimal Power Allocation in Wireless Networks by Local D.C. Programming

https://homepages.laas.fr/henrion/papers/hifoo-haifa.pdf

Multiobjective robust control with HIFOO 2.0

It is known that the design of optimal transmit beamforming vectors for cognitive radio multicast transmission can be formulated as indefinite quadratic optimization programs. Given the challenges of such nonconvex problems, the conventional approach in literature is to recast them as convex semidefinite programs (SDPs) together with rank-one constraints. Then, these nonconvex and discontinuous constraints are dropped allowing for the realization of a pool of relaxed candidate solutions, from which various randomization techniques are utilized with the hope to recover the optimal solutions. However, it has been shown that such approach fails to deliver satisfactory outcomes in many practical settings, wherein the determined solutions are found to be unacceptably far from the actual optimality. On the contrary, we in this contribution tackle the aforementioned optimal beamforming problems differently by representing them as SDPs with additional reverse convex (but continuous) constraints. Nonsmooth optimization algorithms are then proposed to locate the optimal solutions of such design problems in an efficient manner. Our thorough numerical examples verify that the proposed algorithms offer almost global optimality whilst requiring relatively low computational load.

Nonsmooth Optimization for Efficient Beamforming in Cognitive Radio Multicast Transmission

This paper considers joint linear processing at multi-antenna sources and one multiple-input multiple-output (MIMO) relay station for both one-way and two-way relay-assisted wireless communications. The one-way relaying is applicable in the scenario of downlink transmission by a multi-antenna base station to multiple single-antenna users with the help of one MIMO relay. In such a scenario, the objective of join linear processing is to maximize the information throughput to users. The design problem is equivalently formulated as the maximization of the worst signal-to-interference-plus-noise ratio (SINR) among all users subject to various transmission power constraints. Such a program of nonconvex objective minimization under nonconvex constraints is transformed to a canonical d.c. (difference of convex functions/sets) program of d.c. function optimization under convex constraints through nonconvex duality with zero duality gap. An efficient iterative algorithm is then applied to solve this canonical d.c program. For the scenario of using one MIMO relay to assist two sources exchanging their information in two-way relying manner, the joint linear processing aims at either minimizing the maximum mean square error (MSE) or maximizing the total information throughput of the two sources. By applying tractable optimization for the linear minimum MSE estimator and d.c. programming, an iterative algorithm is developed to solve these two optimization problems. Extensive simulation results demonstrate that the proposed methods substantially outperform previously-known joint optimization methods.

Joint Optimization of Source Precoding and Relay Beamforming in Wireless MIMO Relay Networks

We present a new approach to mixed 2 /H ∞ output feedback control synthesis. Our method uses nonsmooth mathematical programming techniques to compute locally optimal 2 /H ∞ -controllers, which may have a predefined structure. We prove global convergence of our method and present numerical tests to validate it numerically.

/pdf/mixed-h-2-h-control-via-nonsmooth-optimization-2my5vbmaa6.pdf

Mixed H 2 /H ∞ control via nonsmooth optimization

We present a new approach to mixed $H_2/H_\infty$ output feedback control synthesis. Our method uses nonsmooth mathematical programming techniques to compute locally optimal $H_2/H_\infty$-controllers, which may have a predefined structure. We prove global convergence of our method and present tests to validate it numerically.

/pdf/mixed-h-2-h-infty-control-via-nonsmooth-optimization-3du8wmqjgu.pdf

Mixed $H_2/H_\infty$ Control via Nonsmooth Optimization

The mixed H2/Hinfin synthesis problem is addressed via nonsmooth mathematical programming. The proposed algorithm is of first order and can handle any controller structure of practical interest. Since computations are carried out in the frequency domain, the method does not suffer dimensional restrictions like LMI or BMI methods. Global convergence is established and several numerical tests are presented.

/pdf/nonsmooth-optimization-algorithm-for-mixed-h-2-h-synthesis-ez1spcxsdb.pdf

A. Rondepierre

Papers

Mixed $H_2/H_\infty$ Control via Nonsmooth Optimization

Nonsmooth optimization algorithm for mixed H 2 /H ∞ synthesis