Global Optimization for a Class of Nonlinear Sum of Ratios Problem

We present a branch and bound algorithm for globally solving the sum of ratios problem. In this problem, each term in the objective function is a ratio of two functions which are the sums of the absolute values of affine functions with coefficients. This problem has an important application in financial optimization, but the global optimization algorithm for this problem is still rare in the literature so far. In the algorithm we presented, the branch and bound search undertaken by the algorithm uses rectangular partitioning and takes place in a space which typically has a much smaller dimension than the space to which the decision variables of this problem belong. Convergence of the algorithm is shown. At last, some numerical examples are given to vindicate our conclusions

Optimal exact designs of experiments via Mixed Integer Nonlinear Programming

Optimal exact designs are problematic to find and study because there is no unified theory for determining them and studyingtheir properties. Each has its own challenges and when a method exists to confirm the design optimality, it is invariablyapplicable to the particular problem only.We propose a systematic approach to construct optimal exact designs by incorporatingthe Cholesky decomposition of the Fisher Information Matrix in a Mixed Integer Nonlinear Programming formulation. Asexamples, we apply the methodology to find D- and A-optimal exact designs for linear and nonlinear models using global orlocal optimizers. Our examples include design problems with constraints on the locations or the number of replicates at theoptimal design points

Power Allocation and Scheduling for SWIPT Systems with Non-linear Energy Harvesting Model

In this paper, we design a resource allocation algorithm for multiuser simultaneous wireless information and power transfer systems for a realistic non-linear energy harvesting (EH) model. In particular, the algorithm design is formulated as a non-convex optimization problem for the maximization of the long-term average total harvested power at EH receivers subject to quality of service requirements for information decoding receivers. To obtain a tractable solution, we transform the corresponding non-convex sum-of-ratios objective function into an equivalent objective function in parametric subtractive form. This leads to a computationally efficient iterative resource allocation algorithm. Numerical results reveal a significant performance gain that can be achieved if the resource allocation algorithm design is based on the non-linear EH model instead of the traditional linear model.Comment: Accepted for presentation at the IEEE ICC 201