Sum-Rate Maximization in Two-Way AF MIMO Relaying: Polynomial Time Solutions to a Class of DC Programming Problems

Sum-rate maximization in two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying belongs to the class of difference-of-convex functions (DC) programming problems. DC programming problems occur as well in other signal processing applications and are typically solved using different modifications of the branch-and-bound method. This method, however, does not have any polynomial time complexity guarantees. In this paper, we show that a class of DC programming problems, to which the sum-rate maximization in two-way MIMO relaying belongs, can be solved very efficiently in polynomial time, and develop two algorithms. The objective function of the problem is represented as a product of quadratic ratios and parameterized so that its convex part (versus the concave part) contains only one (or two) optimization variables. One of the algorithms is called POlynomial-Time DC (POTDC) and is based on semi-definite programming (SDP) relaxation, linearization, and an iterative search over a single parameter. The other algorithm is called RAte-maximization via Generalized EigenvectorS (RAGES) and is based on the generalized eigenvectors method and an iterative search over two (or one, in its approximate version) optimization variables. We also derive an upper-bound for the optimal values of the corresponding optimization problem and show by simulations that this upper-bound can be achieved by both algorithms. The proposed methods for maximizing the sum-rate in the two-way AF MIMO relaying system are shown to be superior to other state-of-the-art algorithms.Comment: 35 pages, 10 figures, Submitted to the IEEE Trans. Signal Processing in Nov. 201

Engineering design applications of surrogate-assisted optimization techniques

The construction of models aimed at learning the behaviour of a system whose responses to inputs are expensive to measure is a branch of statistical science that has been around for a very long time. Geostatistics has pioneered a drive over the last half century towards a better understanding of the accuracy of such ‘surrogate’ models of the expensive function. Of particular interest to us here are some of the even more recent advances related to exploiting such formulations in an optimization context. While the classic goal of the modelling process has been to achieve a uniform prediction accuracy across the domain, an economical optimization process may aim to bias the distribution of the learning budget towards promising basins of attraction. This can only happen, of course, at the expense of the global exploration of the space and thus finding the best balance may be viewed as an optimization problem in itself. We examine here a selection of the state of-the-art solutions to this type of balancing exercise through the prism of several simple, illustrative problems, followed by two ‘real world’ applications: the design of a regional airliner wing and the multi-objective search for a low environmental impact hous

Spatial optimization for land use allocation: accounting for sustainability concerns

Land-use allocation has long been an important area of research in regional science. Land-use patterns are fundamental to the functions of the biosphere, creating interactions that have substantial impacts on the environment. The spatial arrangement of land uses therefore has implications for activity and travel within a region. Balancing development, economic growth, social interaction, and the protection of the natural environment is at the heart of long-term sustainability. Since land-use patterns are spatially explicit in nature, planning and management necessarily must integrate geographical information system and spatial optimization in meaningful ways if efficiency goals and objectives are to be achieved. This article reviews spatial optimization approaches that have been relied upon to support land-use planning. Characteristics of sustainable land use, particularly compactness, contiguity, and compatibility, are discussed and how spatial optimization techniques have addressed these characteristics are detailed. In particular, objectives and constraints in spatial optimization approaches are examined